premise
stringlengths 940
1.64k
| hypothesis
stringclasses 224
values | label
stringclasses 3
values | premise_tptp
stringlengths 721
1.28k
| hypothesis_tptp
stringclasses 224
values | proof_inputs
sequencelengths 0
15
| proof
stringlengths 684
15.9k
⌀ | rule_concentration
int64 0
0
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|---|---|---|---|---|---|---|---|
If someone is both not patient and wise then someone is both not creative and humble.
If someone is both not generous and brave then alice is old.
If fred is kind or generous then paul is quiet or curious and vice versa.
Everyone who is either kind or curious is both funny and not curious.
If susan is both not strong and not brave then susan is not rich.
Everyone who is either curious or not curious is both not old and not generous and vice versa.
Everyone who is both calm and not patient is both not patient and not wise.
Everyone who is either old or humble is either not creative or happy.
If someone is generous or not calm then paul is calm.
Everyone who is either not brave or not rich is not funny and vice versa.
Everyone who is funny is tall and vice versa.
If alice is not wise or strong then paul is both not patient and quiet.
If lucy is both tall and funny then lucy is both patient and curious.
Everyone who is old or funny is both not creative and brave and vice versa.
Everyone who is generous or quiet is both quiet and calm.
If mary is not curious or not happy then someone is both not old and happy and vice versa.
Someone is old or not tall.
Fred is either not quiet or not curious.
John is curious or not calm.
Someone is either not quiet or not strong.
Someone is either not rich or rich.
Someone is either tall or kind. | Mary is not funny. | entailment | ((?[X]:((~patient(X)&wise(X))))=>(?[X]:((~creative(X)&humble(X)))))&
((?[X]:((~generous(X)&brave(X))))=>(old(alice)))&
(((kind(fred)|generous(fred)))<=>((quiet(paul)|curious(paul))))&
(![X]:((kind(X)<~>curious(X))=>(funny(X)&~curious(X))))&
(((~strong(susan)&~brave(susan)))=>(~rich(susan)))&
(![X]:((curious(X)<~>~curious(X))<=>(~old(X)&~generous(X))))&
(![X]:((calm(X)&~patient(X))=>(~patient(X)&~wise(X))))&
(![X]:((old(X)<~>humble(X))=>(~creative(X)<~>happy(X))))&
((?[X]:((generous(X)|~calm(X))))=>(calm(paul)))&
(![X]:((~brave(X)<~>~rich(X))<=>~funny(X)))&
(![X]:(funny(X)<=>tall(X)))&
(((~wise(alice)|strong(alice)))=>((~patient(paul)&quiet(paul))))&
(((tall(lucy)&funny(lucy)))=>((patient(lucy)&curious(lucy))))&
(![X]:((old(X)|funny(X))<=>(~creative(X)&brave(X))))&
(![X]:((generous(X)|quiet(X))=>(quiet(X)&calm(X))))&
(((~curious(mary)|~happy(mary)))<=>(?[X]:((~old(X)&happy(X)))))&
(?[X]:((old(X)|~tall(X))))&
((~quiet(fred)<~>~curious(fred)))&
((curious(john)|~calm(john)))&
(?[X]:((~quiet(X)<~>~strong(X))))&
(?[X]:((~rich(X)<~>rich(X))))&
(?[X]:((tall(X)<~>kind(X)))) | ~funny(mary) | [
"p1",
"p5",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 7860803489962887403195128
% SZS output start Proof for 7860803489962887403195128
2. ? [X0] : (brave(X0) & ~generous(X0)) => old(alice) [input p1]
6. ! [X0] : ((curious(X0) <~> ~curious(X0)) <=> (~generous(X0) & ~old(X0))) [input p5]
14. ! [X0] : ((funny(X0) | old(X0)) <=> (brave(X0) & ~creative(X0))) [input p13]
23. funny(mary) [input hypothesis]
26. old(alice) | ! [X0] : (~brave(X0) | generous(X0)) [ennf transformation 2]
44. ! [X0] : ((((curious(X0) | ~curious(X0)) & (~curious(X0) | curious(X0))) | (generous(X0) | old(X0))) & ((~generous(X0) & ~old(X0)) | ((curious(X0) | curious(X0)) & (~curious(X0) | ~curious(X0))))) [nnf transformation 6]
45. ! [X0] : ((((curious(X0) | ~curious(X0)) & (~curious(X0) | curious(X0))) | generous(X0) | old(X0)) & ((~generous(X0) & ~old(X0)) | ((curious(X0) | curious(X0)) & (~curious(X0) | ~curious(X0))))) [flattening 44]
49. ! [X0] : (((funny(X0) | old(X0)) | (~brave(X0) | creative(X0))) & ((brave(X0) & ~creative(X0)) | (~funny(X0) & ~old(X0)))) [nnf transformation 14]
50. ! [X0] : ((funny(X0) | old(X0) | ~brave(X0) | creative(X0)) & ((brave(X0) & ~creative(X0)) | (~funny(X0) & ~old(X0)))) [flattening 49]
70. old(alice) | ~brave(X0) | generous(X0) [cnf transformation 26]
80. ~old(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 45]
81. ~old(X0) | curious(X0) | curious(X0) [cnf transformation 45]
82. ~generous(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 45]
83. ~generous(X0) | curious(X0) | curious(X0) [cnf transformation 45]
109. ~funny(X0) | brave(X0) [cnf transformation 50]
130. funny(mary) [cnf transformation 23]
131. ~old(X0) | ~curious(X0) [duplicate literal removal 80]
132. ~old(X0) | curious(X0) [duplicate literal removal 81]
133. ~generous(X0) | ~curious(X0) [duplicate literal removal 82]
134. ~generous(X0) | curious(X0) [duplicate literal removal 83]
150. 4 <=> ! [X0] : (~brave(X0) | generous(X0)) [avatar definition]
151. ~brave(X0) | generous(X0) <- (4) [avatar component clause 150]
153. 5 <=> old(alice) [avatar definition]
155. old(alice) <- (5) [avatar component clause 153]
156. 4 | 5 [avatar split clause 70,153,150]
190. ~generous(X0) [subsumption resolution 133,134]
191. ~old(X0) [subsumption resolution 131,132]
294. ~brave(X0) <- (4) [subsumption resolution 151,190]
305. brave(mary) [resolution 109,130]
307. $false <- (4) [subsumption resolution 305,294]
308. ~4 [avatar contradiction clause 307]
311. $false <- (5) [subsumption resolution 155,191]
312. ~5 [avatar contradiction clause 311]
313. $false [avatar sat refutation 156,308,312]
% SZS output end Proof for 7860803489962887403195128
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If john is not rich or not creative then someone is both tall and not wise and vice versa. If someone is both not patient and not kind then john is both generous and not happy. If paul is not calm then susan is not patient or not quiet and vice versa. If mary is patient then lucy is not humble. If someone is either not patient or not kind then fred is both not creative and not old. Everyone who is both tall and curious is calm and vice versa. If someone is patient or not happy then someone is both generous and happy and vice versa. Everyone who is both strong and not generous is curious and vice versa. Everyone who is wise or humble is both not creative and happy and vice versa. Everyone who is either not rich or happy is kind or not generous and vice versa. Everyone who is not funny or calm is old or not old. If someone is both not humble and not funny then someone is not funny. Everyone who is wise is old or tall. If someone is creative then susan is not calm and vice versa. Everyone who is either rich or not wise is not generous and vice versa. Everyone who is not generous or happy is either not creative or rich. Someone is wise or old. Paul is both not creative and not curious. Someone is quiet or not funny. Someone is both not quiet and strong. Someone is both creative and not quiet. Someone is not tall or not old. Lucy is either strong or tall. Fred is both rich and not patient. | John is creative. | neutral | (((~rich(john)|~creative(john)))<=>(?[X]:((tall(X)&~wise(X)))))&
((?[X]:((~patient(X)&~kind(X))))=>((generous(john)&~happy(john))))&
((~calm(paul))<=>((~patient(susan)|~quiet(susan))))&
((patient(mary))=>(~humble(lucy)))&
((?[X]:((~patient(X)<~>~kind(X))))=>((~creative(fred)&~old(fred))))&
(![X]:((tall(X)&curious(X))<=>calm(X)))&
((?[X]:((patient(X)|~happy(X))))<=>(?[X]:((generous(X)&happy(X)))))&
(![X]:((strong(X)&~generous(X))<=>curious(X)))&
(![X]:((wise(X)|humble(X))<=>(~creative(X)&happy(X))))&
(![X]:((~rich(X)<~>happy(X))<=>(kind(X)|~generous(X))))&
(![X]:((~funny(X)|calm(X))=>(old(X)|~old(X))))&
((?[X]:((~humble(X)&~funny(X))))=>(?[X]:(~funny(X))))&
(![X]:(wise(X)=>(old(X)|tall(X))))&
((?[X]:(creative(X)))<=>(~calm(susan)))&
(![X]:((rich(X)<~>~wise(X))<=>~generous(X)))&
(![X]:((~generous(X)|happy(X))=>(~creative(X)<~>rich(X))))&
(?[X]:((wise(X)|old(X))))&
((~creative(paul)&~curious(paul)))&
(?[X]:((quiet(X)|~funny(X))))&
(?[X]:((~quiet(X)&strong(X))))&
(?[X]:((creative(X)&~quiet(X))))&
(?[X]:((~tall(X)|~old(X))))&
((strong(lucy)<~>tall(lucy)))&
((rich(fred)&~patient(fred))) | creative(john) | [] | null | 0 |
If someone is both curious and kind then someone is tall or calm. Everyone who is old or tall is humble. Everyone who is either generous or not happy is curious or rich. Everyone who is both patient and not generous is not quiet and vice versa. Everyone who is not strong is not generous and vice versa. Everyone who is not humble is either happy or creative and vice versa. If susan is not kind or not rich then susan is either not curious or not patient and vice versa. Everyone who is not old is either not happy or patient. Everyone who is kind or not rich is either not happy or not generous and vice versa. Everyone who is either not creative or not quiet is both creative and strong and vice versa. If lucy is either humble or rich then paul is humble or not calm. Everyone who is both not generous and not curious is either wise or not happy and vice versa. Everyone who is not patient or quiet is both wise and not humble and vice versa. If someone is tall or not funny then someone is not humble and vice versa. If alice is either creative or rich then paul is not generous. Everyone who is curious or humble is both not wise and not quiet. Lucy is not rich or calm. Someone is humble. Someone is calm. Paul is both happy and curious. Fred is patient or not curious. | Paul is old. | contradiction | ((?[X]:((curious(X)&kind(X))))=>(?[X]:((tall(X)|calm(X)))))&
(![X]:((old(X)|tall(X))=>humble(X)))&
(![X]:((generous(X)<~>~happy(X))=>(curious(X)|rich(X))))&
(![X]:((patient(X)&~generous(X))<=>~quiet(X)))&
(![X]:(~strong(X)<=>~generous(X)))&
(![X]:(~humble(X)<=>(happy(X)<~>creative(X))))&
(((~kind(susan)|~rich(susan)))<=>((~curious(susan)<~>~patient(susan))))&
(![X]:(~old(X)=>(~happy(X)<~>patient(X))))&
(![X]:((kind(X)|~rich(X))<=>(~happy(X)<~>~generous(X))))&
(![X]:((~creative(X)<~>~quiet(X))<=>(creative(X)&strong(X))))&
(((humble(lucy)<~>rich(lucy)))=>((humble(paul)|~calm(paul))))&
(![X]:((~generous(X)&~curious(X))<=>(wise(X)<~>~happy(X))))&
(![X]:((~patient(X)|quiet(X))<=>(wise(X)&~humble(X))))&
((?[X]:((tall(X)|~funny(X))))<=>(?[X]:(~humble(X))))&
(((creative(alice)<~>rich(alice)))=>(~generous(paul)))&
(![X]:((curious(X)|humble(X))=>(~wise(X)&~quiet(X))))&
((~rich(lucy)|calm(lucy)))&
(?[X]:(humble(X)))&
(?[X]:(calm(X)))&
((happy(paul)&curious(paul)))&
((patient(fred)|~curious(fred))) | old(paul) | [
"p1",
"p3",
"p4",
"p5",
"p9",
"p15",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 922095623848071070894168
% SZS output start Proof for 922095623848071070894168
2. ! [X0] : ((tall(X0) | old(X0)) => humble(X0)) [input p1]
4. ! [X0] : ((~generous(X0) & patient(X0)) <=> ~quiet(X0)) [input p3]
5. ! [X0] : (~strong(X0) <=> ~generous(X0)) [input p4]
6. ! [X0] : (~humble(X0) <=> (happy(X0) <~> creative(X0))) [input p5]
10. ! [X0] : ((~creative(X0) <~> ~quiet(X0)) <=> (strong(X0) & creative(X0))) [input p9]
16. ! [X0] : ((humble(X0) | curious(X0)) => (~quiet(X0) & ~wise(X0))) [input p15]
20. curious(paul) & happy(paul) [input p19]
22. old(paul) [input hypothesis]
26. ! [X0] : (humble(X0) | (~tall(X0) & ~old(X0))) [ennf transformation 2]
33. ! [X0] : ((~quiet(X0) & ~wise(X0)) | (~humble(X0) & ~curious(X0))) [ennf transformation 16]
38. ! [X0] : (((~generous(X0) & patient(X0)) | quiet(X0)) & (~quiet(X0) | (generous(X0) | ~patient(X0)))) [nnf transformation 4]
39. ! [X0] : (((~generous(X0) & patient(X0)) | quiet(X0)) & (~quiet(X0) | generous(X0) | ~patient(X0))) [flattening 38]
40. ! [X0] : ((~strong(X0) | generous(X0)) & (~generous(X0) | strong(X0))) [nnf transformation 5]
41. ! [X0] : ((~humble(X0) | ((happy(X0) | ~creative(X0)) & (creative(X0) | ~happy(X0)))) & (((~creative(X0) | ~happy(X0)) & (creative(X0) | happy(X0))) | humble(X0))) [nnf transformation 6]
47. ! [X0] : ((((quiet(X0) | creative(X0)) & (~quiet(X0) | ~creative(X0))) | (~strong(X0) | ~creative(X0))) & ((strong(X0) & creative(X0)) | ((~creative(X0) | quiet(X0)) & (~quiet(X0) | creative(X0))))) [nnf transformation 10]
48. ! [X0] : ((((quiet(X0) | creative(X0)) & (~quiet(X0) | ~creative(X0))) | ~strong(X0) | ~creative(X0)) & ((strong(X0) & creative(X0)) | ((~creative(X0) | quiet(X0)) & (~quiet(X0) | creative(X0))))) [flattening 47]
65. ~old(X0) | humble(X0) [cnf transformation 26]
71. ~generous(X0) | quiet(X0) [cnf transformation 39]
73. ~strong(X0) | generous(X0) [cnf transformation 40]
76. ~happy(X0) | creative(X0) | ~humble(X0) [cnf transformation 41]
95. ~creative(X0) | strong(X0) | quiet(X0) [cnf transformation 48]
118. ~quiet(X0) | ~curious(X0) [cnf transformation 33]
123. happy(paul) [cnf transformation 20]
124. curious(paul) [cnf transformation 20]
126. old(paul) [cnf transformation 22]
172. 10 <=> humble(paul) [avatar definition]
174. humble(paul) <- (10) [avatar component clause 172]
215. 20 <=> generous(paul) [avatar definition]
216. generous(paul) <- (20) [avatar component clause 215]
234. humble(paul) [resolution 65,126]
235. 10 [avatar split clause 234,172]
252. creative(paul) | ~humble(paul) [resolution 76,123]
253. creative(paul) <- (10) [subsumption resolution 252,174]
323. strong(paul) | quiet(paul) <- (10) [resolution 95,253]
325. 33 <=> quiet(paul) [avatar definition]
326. ~quiet(paul) <- (~33) [avatar component clause 325]
327. quiet(paul) <- (33) [avatar component clause 325]
329. 34 <=> strong(paul) [avatar definition]
331. strong(paul) <- (34) [avatar component clause 329]
332. 33 | 34 | ~10 [avatar split clause 323,172,329,325]
345. ~curious(paul) <- (33) [resolution 327,118]
351. $false <- (33) [subsumption resolution 345,124]
352. ~33 [avatar contradiction clause 351]
358. generous(paul) <- (34) [resolution 331,73]
361. 20 | ~34 [avatar split clause 358,329,215]
391. quiet(paul) <- (20) [resolution 216,71]
392. $false <- (20, ~33) [subsumption resolution 391,326]
393. ~20 | 33 [avatar contradiction clause 392]
394. $false [avatar sat refutation 235,332,352,361,393]
% SZS output end Proof for 922095623848071070894168
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.034 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not happy or curious is both funny and humble and vice versa.
Everyone who is both not quiet and generous is not happy or old and vice versa.
If someone is not tall then alice is both curious and not patient.
If someone is either not kind or wise then john is quiet or rich.
If alice is both patient and not humble then someone is both not creative and not calm.
If someone is either not curious or not calm then susan is either not creative or wise.
If someone is curious then someone is wise or not tall and vice versa.
Everyone who is both not brave and not kind is not patient or old.
If mary is happy or not happy then someone is not patient and vice versa.
Everyone who is either patient or curious is strong.
Everyone who is calm or old is either kind or not strong.
If susan is either happy or not strong then someone is patient.
Everyone who is quiet or old is not happy or old and vice versa.
Everyone who is either quiet or not tall is either not happy or patient and vice versa.
If someone is kind then john is both not rich and not happy and vice versa.
If john is not strong or funny then mary is both brave and not brave and vice versa.
Someone is not brave.
Someone is curious.
Paul is quiet or not generous.
Someone is tall.
Someone is patient or not wise.
Someone is both not brave and generous.
Someone is not humble or not quiet. | Paul is quiet. | contradiction | (![X]:((~happy(X)<~>curious(X))<=>(funny(X)&humble(X))))&
(![X]:((~quiet(X)&generous(X))<=>(~happy(X)|old(X))))&
((?[X]:(~tall(X)))=>((curious(alice)&~patient(alice))))&
((?[X]:((~kind(X)<~>wise(X))))=>((quiet(john)|rich(john))))&
(((patient(alice)&~humble(alice)))=>(?[X]:((~creative(X)&~calm(X)))))&
((?[X]:((~curious(X)<~>~calm(X))))=>((~creative(susan)<~>wise(susan))))&
((?[X]:(curious(X)))<=>(?[X]:((wise(X)|~tall(X)))))&
(![X]:((~brave(X)&~kind(X))=>(~patient(X)|old(X))))&
(((happy(mary)|~happy(mary)))<=>(?[X]:(~patient(X))))&
(![X]:((patient(X)<~>curious(X))=>strong(X)))&
(![X]:((calm(X)|old(X))=>(kind(X)<~>~strong(X))))&
(((happy(susan)<~>~strong(susan)))=>(?[X]:(patient(X))))&
(![X]:((quiet(X)|old(X))<=>(~happy(X)|old(X))))&
(![X]:((quiet(X)<~>~tall(X))<=>(~happy(X)<~>patient(X))))&
((?[X]:(kind(X)))<=>((~rich(john)&~happy(john))))&
(((~strong(john)|funny(john)))<=>((brave(mary)&~brave(mary))))&
(?[X]:(~brave(X)))&
(?[X]:(curious(X)))&
((quiet(paul)|~generous(paul)))&
(?[X]:(tall(X)))&
(?[X]:((patient(X)|~wise(X))))&
(?[X]:((~brave(X)&generous(X))))&
(?[X]:((~humble(X)|~quiet(X)))) | quiet(paul) | [
"p1",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 2465280531223870856460017
% SZS output start Proof for 2465280531223870856460017
2. ! [X0] : ((generous(X0) & ~quiet(X0)) <=> (old(X0) | ~happy(X0))) [input p1]
13. ! [X0] : ((old(X0) | quiet(X0)) <=> (old(X0) | ~happy(X0))) [input p12]
24. quiet(paul) [input hypothesis]
39. ! [X0] : (((generous(X0) & ~quiet(X0)) | (~old(X0) & happy(X0))) & ((old(X0) | ~happy(X0)) | (~generous(X0) | quiet(X0)))) [nnf transformation 2]
40. ! [X0] : (((generous(X0) & ~quiet(X0)) | (~old(X0) & happy(X0))) & (old(X0) | ~happy(X0) | ~generous(X0) | quiet(X0))) [flattening 39]
60. ! [X0] : (((old(X0) | quiet(X0)) | (~old(X0) & happy(X0))) & ((old(X0) | ~happy(X0)) | (~old(X0) & ~quiet(X0)))) [nnf transformation 13]
61. ! [X0] : ((old(X0) | quiet(X0) | (~old(X0) & happy(X0))) & (old(X0) | ~happy(X0) | (~old(X0) & ~quiet(X0)))) [flattening 60]
89. ~quiet(X0) | happy(X0) [cnf transformation 40]
90. ~quiet(X0) | ~old(X0) [cnf transformation 40]
118. old(X0) | ~happy(X0) | ~quiet(X0) [cnf transformation 61]
146. quiet(paul) [cnf transformation 24]
254. old(X0) | ~quiet(X0) [subsumption resolution 118,89]
255. ~quiet(X0) [subsumption resolution 254,90]
300. $false [subsumption resolution 146,255]
% SZS output end Proof for 2465280531223870856460017
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If susan is not rich then lucy is both wise and generous. Everyone who is not humble is not quiet and vice versa. Everyone who is either not strong or wise is either not humble or not calm. Everyone who is quiet is not kind or humble and vice versa. Everyone who is quiet or not rich is old or not humble. Everyone who is not funny or kind is both quiet and not creative. Everyone who is not kind is wise and vice versa. Everyone who is either funny or calm is not brave or quiet. If someone is not happy then alice is either not rich or not quiet. Everyone who is both not humble and not generous is either not rich or not old and vice versa. If someone is both not quiet and not brave then someone is both not wise and not quiet and vice versa. If someone is generous or tall then alice is strong and vice versa. Everyone who is not happy is brave or humble. Everyone who is not happy or not funny is both creative and quiet. Everyone who is not patient is both not kind and happy and vice versa. Someone is brave or wise. Susan is both brave and not strong. Someone is kind or happy. Someone is both not kind and not creative. Alice is not tall or not old. Someone is not calm or funny. Mary is not rich or curious. | Alice is not humble. | contradiction | ((~rich(susan))=>((wise(lucy)&generous(lucy))))&
(![X]:(~humble(X)<=>~quiet(X)))&
(![X]:((~strong(X)<~>wise(X))=>(~humble(X)<~>~calm(X))))&
(![X]:(quiet(X)<=>(~kind(X)|humble(X))))&
(![X]:((quiet(X)|~rich(X))=>(old(X)|~humble(X))))&
(![X]:((~funny(X)|kind(X))=>(quiet(X)&~creative(X))))&
(![X]:(~kind(X)<=>wise(X)))&
(![X]:((funny(X)<~>calm(X))=>(~brave(X)|quiet(X))))&
((?[X]:(~happy(X)))=>((~rich(alice)<~>~quiet(alice))))&
(![X]:((~humble(X)&~generous(X))<=>(~rich(X)<~>~old(X))))&
((?[X]:((~quiet(X)&~brave(X))))<=>(?[X]:((~wise(X)&~quiet(X)))))&
((?[X]:((generous(X)|tall(X))))<=>(strong(alice)))&
(![X]:(~happy(X)=>(brave(X)|humble(X))))&
(![X]:((~happy(X)|~funny(X))=>(creative(X)&quiet(X))))&
(![X]:(~patient(X)<=>(~kind(X)&happy(X))))&
(?[X]:((brave(X)|wise(X))))&
((brave(susan)&~strong(susan)))&
(?[X]:((kind(X)|happy(X))))&
(?[X]:((~kind(X)&~creative(X))))&
((~tall(alice)|~old(alice)))&
(?[X]:((~calm(X)|funny(X))))&
((~rich(mary)|curious(mary))) | ~humble(alice) | [
"p1",
"p3",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 1086871409247646467322234
% SZS output start Proof for 1086871409247646467322234
2. ! [X0] : (~humble(X0) <=> ~quiet(X0)) [input p1]
4. ! [X0] : (quiet(X0) <=> (humble(X0) | ~kind(X0))) [input p3]
6. ! [X0] : ((kind(X0) | ~funny(X0)) => (~creative(X0) & quiet(X0))) [input p5]
23. ~humble(alice) [input hypothesis]
34. ! [X0] : ((~creative(X0) & quiet(X0)) | (~kind(X0) & funny(X0))) [ennf transformation 6]
38. ! [X0] : ((~humble(X0) | quiet(X0)) & (~quiet(X0) | humble(X0))) [nnf transformation 2]
40. ! [X0] : ((quiet(X0) | (~humble(X0) & kind(X0))) & ((humble(X0) | ~kind(X0)) | ~quiet(X0))) [nnf transformation 4]
41. ! [X0] : ((quiet(X0) | (~humble(X0) & kind(X0))) & (humble(X0) | ~kind(X0) | ~quiet(X0))) [flattening 40]
63. ~quiet(X0) | humble(X0) [cnf transformation 38]
70. quiet(X0) | kind(X0) [cnf transformation 41]
75. quiet(X0) | ~kind(X0) [cnf transformation 34]
104. ~humble(alice) [cnf transformation 23]
120. quiet(X0) [subsumption resolution 75,70]
164. humble(X0) [resolution 63,120]
165. $false [resolution 164,104]
% SZS output end Proof for 1086871409247646467322234
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 4989
% Time elapsed: 0.019 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not happy is humble or not strong and vice versa. If john is not humble then paul is both not humble and kind. Everyone who is tall is curious. If someone is not calm then lucy is wise and vice versa. Everyone who is both not humble and patient is either not curious or not calm. Everyone who is both humble and not creative is both not strong and brave. Everyone who is humble or happy is both not tall and generous. Everyone who is both strong and generous is either not happy or not generous. Everyone who is both strong and not strong is both old and wise. If mary is not creative or patient then lucy is either humble or not tall and vice versa. Everyone who is wise or not strong is not wise and vice versa. If john is either not happy or not rich then mary is not happy or not curious. Everyone who is not old is rich. If paul is kind then john is both old and not tall and vice versa. Everyone who is not quiet is both generous and not happy and vice versa. Everyone who is both creative and happy is both creative and not generous and vice versa. Fred is both not rich and tall. John is either rich or quiet. Alice is not happy or not brave. Someone is either not old or humble. Someone is not patient or wise. Someone is not happy. | Paul is strong. | contradiction | (![X]:(~happy(X)<=>(humble(X)|~strong(X))))&
((~humble(john))=>((~humble(paul)&kind(paul))))&
(![X]:(tall(X)=>curious(X)))&
((?[X]:(~calm(X)))<=>(wise(lucy)))&
(![X]:((~humble(X)&patient(X))=>(~curious(X)<~>~calm(X))))&
(![X]:((humble(X)&~creative(X))=>(~strong(X)&brave(X))))&
(![X]:((humble(X)|happy(X))=>(~tall(X)&generous(X))))&
(![X]:((strong(X)&generous(X))=>(~happy(X)<~>~generous(X))))&
(![X]:((strong(X)&~strong(X))=>(old(X)&wise(X))))&
(((~creative(mary)|patient(mary)))<=>((humble(lucy)<~>~tall(lucy))))&
(![X]:((wise(X)|~strong(X))<=>~wise(X)))&
(((~happy(john)<~>~rich(john)))=>((~happy(mary)|~curious(mary))))&
(![X]:(~old(X)=>rich(X)))&
((kind(paul))<=>((old(john)&~tall(john))))&
(![X]:(~quiet(X)<=>(generous(X)&~happy(X))))&
(![X]:((creative(X)&happy(X))<=>(creative(X)&~generous(X))))&
((~rich(fred)&tall(fred)))&
((rich(john)<~>quiet(john)))&
((~happy(alice)|~brave(alice)))&
(?[X]:((~old(X)<~>humble(X))))&
(?[X]:((~patient(X)|wise(X))))&
(?[X]:(~happy(X))) | strong(paul) | [
"p10",
"hypothesis"
] | % SZS status Unsatisfiable for 4700249153489257576677907
% SZS output start Proof for 4700249153489257576677907
11. ! [X0] : ((~strong(X0) | wise(X0)) <=> ~wise(X0)) [input p10]
23. strong(paul) [input hypothesis]
48. ! [X0] : (((~strong(X0) | wise(X0)) | wise(X0)) & (~wise(X0) | (strong(X0) & ~wise(X0)))) [nnf transformation 11]
49. ! [X0] : ((~strong(X0) | wise(X0) | wise(X0)) & (~wise(X0) | (strong(X0) & ~wise(X0)))) [flattening 48]
91. ~wise(X0) | ~wise(X0) [cnf transformation 49]
93. ~strong(X0) | wise(X0) | wise(X0) [cnf transformation 49]
116. strong(paul) [cnf transformation 23]
117. ~wise(X0) [duplicate literal removal 91]
118. ~strong(X0) | wise(X0) [duplicate literal removal 93]
217. wise(paul) [resolution 118,116]
218. $false [subsumption resolution 217,117]
% SZS output end Proof for 4700249153489257576677907
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not quiet and generous is not happy or creative and vice versa. Everyone who is calm is quiet and vice versa. Everyone who is tall is either not happy or funny. Everyone who is strong is either kind or not generous. Everyone who is not brave is not creative and vice versa. Everyone who is either not calm or happy is brave and vice versa. If mary is not patient or not creative then someone is both not curious and not humble. If alice is not brave or not funny then lucy is either not patient or curious. Everyone who is creative or funny is both humble and strong and vice versa. Everyone who is brave or not curious is both tall and not curious and vice versa. If someone is calm then someone is both not curious and not calm. If someone is both wise and generous then someone is either happy or not strong. Everyone who is humble is either not patient or wise. If someone is not kind then susan is both tall and not funny and vice versa. Everyone who is either strong or not brave is kind. If someone is happy then lucy is humble or not creative. Someone is either generous or not humble. Paul is either generous or not kind. Someone is not generous or not curious. Someone is wise or not old. Alice is either not rich or not quiet. John is kind or not kind. | Paul is old. | neutral | (![X]:((~quiet(X)&generous(X))<=>(~happy(X)|creative(X))))&
(![X]:(calm(X)<=>quiet(X)))&
(![X]:(tall(X)=>(~happy(X)<~>funny(X))))&
(![X]:(strong(X)=>(kind(X)<~>~generous(X))))&
(![X]:(~brave(X)<=>~creative(X)))&
(![X]:((~calm(X)<~>happy(X))<=>brave(X)))&
(((~patient(mary)|~creative(mary)))=>(?[X]:((~curious(X)&~humble(X)))))&
(((~brave(alice)|~funny(alice)))=>((~patient(lucy)<~>curious(lucy))))&
(![X]:((creative(X)|funny(X))<=>(humble(X)&strong(X))))&
(![X]:((brave(X)|~curious(X))<=>(tall(X)&~curious(X))))&
((?[X]:(calm(X)))=>(?[X]:((~curious(X)&~calm(X)))))&
((?[X]:((wise(X)&generous(X))))=>(?[X]:((happy(X)<~>~strong(X)))))&
(![X]:(humble(X)=>(~patient(X)<~>wise(X))))&
((?[X]:(~kind(X)))<=>((tall(susan)&~funny(susan))))&
(![X]:((strong(X)<~>~brave(X))=>kind(X)))&
((?[X]:(happy(X)))=>((humble(lucy)|~creative(lucy))))&
(?[X]:((generous(X)<~>~humble(X))))&
((generous(paul)<~>~kind(paul)))&
(?[X]:((~generous(X)|~curious(X))))&
(?[X]:((wise(X)|~old(X))))&
((~rich(alice)<~>~quiet(alice)))&
((kind(john)|~kind(john))) | old(paul) | [] | null | 0 |
Everyone who is either patient or not rich is not calm or not rich and vice versa.
Everyone who is not kind is either not calm or rich and vice versa.
Everyone who is either kind or not quiet is funny or rich.
Everyone who is not strong is both not creative and not patient and vice versa.
Everyone who is not kind or not humble is not curious or not quiet and vice versa.
If someone is not creative then someone is funny or not generous and vice versa.
Everyone who is either not creative or not curious is both not strong and not quiet.
If someone is not calm or not kind then paul is both patient and wise and vice versa.
If paul is strong then someone is either brave or not happy and vice versa.
Everyone who is not funny or not curious is brave and vice versa.
If someone is either not brave or not happy then john is humble or quiet.
Everyone who is either wise or not wise is both not rich and brave.
If someone is both not happy and not rich then someone is strong or not quiet and vice versa.
Everyone who is either brave or not funny is not creative or quiet and vice versa.
If mary is not rich then someone is both not tall and quiet.
If mary is not strong then someone is both generous and patient.
Someone is tall or patient.
Someone is either not quiet or not humble.
Someone is brave or funny.
Paul is generous.
Lucy is either not happy or not strong. | Paul is rich. | contradiction | (![X]:((patient(X)<~>~rich(X))<=>(~calm(X)|~rich(X))))&
(![X]:(~kind(X)<=>(~calm(X)<~>rich(X))))&
(![X]:((kind(X)<~>~quiet(X))=>(funny(X)|rich(X))))&
(![X]:(~strong(X)<=>(~creative(X)&~patient(X))))&
(![X]:((~kind(X)|~humble(X))<=>(~curious(X)|~quiet(X))))&
((?[X]:(~creative(X)))<=>(?[X]:((funny(X)|~generous(X)))))&
(![X]:((~creative(X)<~>~curious(X))=>(~strong(X)&~quiet(X))))&
((?[X]:((~calm(X)|~kind(X))))<=>((patient(paul)&wise(paul))))&
((strong(paul))<=>(?[X]:((brave(X)<~>~happy(X)))))&
(![X]:((~funny(X)|~curious(X))<=>brave(X)))&
((?[X]:((~brave(X)<~>~happy(X))))=>((humble(john)|quiet(john))))&
(![X]:((wise(X)<~>~wise(X))=>(~rich(X)&brave(X))))&
((?[X]:((~happy(X)&~rich(X))))<=>(?[X]:((strong(X)|~quiet(X)))))&
(![X]:((brave(X)<~>~funny(X))<=>(~creative(X)|quiet(X))))&
((~rich(mary))=>(?[X]:((~tall(X)&quiet(X)))))&
((~strong(mary))=>(?[X]:((generous(X)&patient(X)))))&
(?[X]:((tall(X)|patient(X))))&
(?[X]:((~quiet(X)<~>~humble(X))))&
(?[X]:((brave(X)|funny(X))))&
(generous(paul))&
((~happy(lucy)<~>~strong(lucy))) | rich(paul) | [
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 6891518876841217180463227
% SZS output start Proof for 6891518876841217180463227
12. ! [X0] : ((wise(X0) <~> ~wise(X0)) => (brave(X0) & ~rich(X0))) [input p11]
22. rich(paul) [input hypothesis]
30. ! [X0] : ((brave(X0) & ~rich(X0)) | (wise(X0) <=> ~wise(X0))) [ennf transformation 12]
59. ! [X0] : ((brave(X0) & ~rich(X0)) | ((wise(X0) | wise(X0)) & (~wise(X0) | ~wise(X0)))) [nnf transformation 30]
119. ~rich(X0) | ~wise(X0) | ~wise(X0) [cnf transformation 59]
120. ~rich(X0) | wise(X0) | wise(X0) [cnf transformation 59]
145. rich(paul) [cnf transformation 22]
146. ~rich(X0) | ~wise(X0) [duplicate literal removal 119]
147. ~rich(X0) | wise(X0) [duplicate literal removal 120]
244. ~rich(X0) [subsumption resolution 146,147]
318. $false [subsumption resolution 145,244]
% SZS output end Proof for 6891518876841217180463227
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If paul is both quiet and curious then someone is not old or patient and vice versa.
If someone is not curious then paul is both creative and old and vice versa.
If susan is either not humble or not generous then fred is not wise or wise.
If someone is not brave then alice is not happy and vice versa.
Everyone who is not strong or not old is not creative.
Everyone who is either curious or creative is either not old or rich and vice versa.
Everyone who is both not creative and not tall is creative or patient.
Everyone who is calm or not calm is curious or happy.
Everyone who is kind is both happy and not calm.
If someone is both old and calm then mary is quiet and vice versa.
If someone is not old then alice is either kind or strong.
Everyone who is either not creative or not brave is wise and vice versa.
Everyone who is not humble is both happy and not brave and vice versa.
Everyone who is either not curious or humble is quiet or kind.
Everyone who is not curious or not quiet is not strong and vice versa.
Everyone who is not creative is both not patient and happy and vice versa.
Someone is not quiet or strong.
Alice is both wise and not quiet.
Someone is both rich and not patient.
Someone is either calm or not wise.
John is both not calm and generous.
Alice is not rich or not old. | Mary is not humble. | contradiction | (((quiet(paul)&curious(paul)))<=>(?[X]:((~old(X)|patient(X)))))&
((?[X]:(~curious(X)))<=>((creative(paul)&old(paul))))&
(((~humble(susan)<~>~generous(susan)))=>((~wise(fred)|wise(fred))))&
((?[X]:(~brave(X)))<=>(~happy(alice)))&
(![X]:((~strong(X)|~old(X))=>~creative(X)))&
(![X]:((curious(X)<~>creative(X))<=>(~old(X)<~>rich(X))))&
(![X]:((~creative(X)&~tall(X))=>(creative(X)|patient(X))))&
(![X]:((calm(X)|~calm(X))=>(curious(X)|happy(X))))&
(![X]:(kind(X)=>(happy(X)&~calm(X))))&
((?[X]:((old(X)&calm(X))))<=>(quiet(mary)))&
((?[X]:(~old(X)))=>((kind(alice)<~>strong(alice))))&
(![X]:((~creative(X)<~>~brave(X))<=>wise(X)))&
(![X]:(~humble(X)<=>(happy(X)&~brave(X))))&
(![X]:((~curious(X)<~>humble(X))=>(quiet(X)|kind(X))))&
(![X]:((~curious(X)|~quiet(X))<=>~strong(X)))&
(![X]:(~creative(X)<=>(~patient(X)&happy(X))))&
(?[X]:((~quiet(X)|strong(X))))&
((wise(alice)&~quiet(alice)))&
(?[X]:((rich(X)&~patient(X))))&
(?[X]:((calm(X)<~>~wise(X))))&
((~calm(john)&generous(john)))&
((~rich(alice)|~old(alice))) | ~humble(mary) | [
"p3",
"p4",
"p12",
"p14",
"p15",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 6674803765604290338976318
% SZS output start Proof for 6674803765604290338976318
4. ? [X0] : ~brave(X0) <=> ~happy(alice) [input p3]
5. ! [X0] : ((~old(X0) | ~strong(X0)) => ~creative(X0)) [input p4]
13. ! [X0] : (~humble(X0) <=> (~brave(X0) & happy(X0))) [input p12]
15. ! [X0] : ((~quiet(X0) | ~curious(X0)) <=> ~strong(X0)) [input p14]
16. ! [X0] : (~creative(X0) <=> (happy(X0) & ~patient(X0))) [input p15]
18. ~quiet(alice) & wise(alice) [input p17]
23. ~humble(mary) [input hypothesis]
27. ! [X0] : (~creative(X0) | (old(X0) & strong(X0))) [ennf transformation 5]
45. (? [X0] : ~brave(X0) | happy(alice)) & (~happy(alice) | ! [X0] : brave(X0)) [nnf transformation 4]
46. (? [X0] : ~brave(X0) | happy(alice)) & (~happy(alice) | ! [X1] : brave(X1)) [rectify 45]
47. ? [X0] : ~brave(X0) => ~brave(sK2) [choice axiom]
48. (~brave(sK2) | happy(alice)) & (~happy(alice) | ! [X1] : brave(X1)) [skolemisation 46,47]
56. ! [X0] : ((~humble(X0) | (brave(X0) | ~happy(X0))) & ((~brave(X0) & happy(X0)) | humble(X0))) [nnf transformation 13]
57. ! [X0] : ((~humble(X0) | brave(X0) | ~happy(X0)) & ((~brave(X0) & happy(X0)) | humble(X0))) [flattening 56]
59. ! [X0] : (((~quiet(X0) | ~curious(X0)) | strong(X0)) & (~strong(X0) | (quiet(X0) & curious(X0)))) [nnf transformation 15]
60. ! [X0] : ((~quiet(X0) | ~curious(X0) | strong(X0)) & (~strong(X0) | (quiet(X0) & curious(X0)))) [flattening 59]
61. ! [X0] : ((~creative(X0) | (~happy(X0) | patient(X0))) & ((happy(X0) & ~patient(X0)) | creative(X0))) [nnf transformation 16]
62. ! [X0] : ((~creative(X0) | ~happy(X0) | patient(X0)) & ((happy(X0) & ~patient(X0)) | creative(X0))) [flattening 61]
80. ~happy(alice) | brave(X1) [cnf transformation 48]
82. ~creative(X0) | strong(X0) [cnf transformation 27]
106. ~brave(X0) | humble(X0) [cnf transformation 57]
111. ~strong(X0) | quiet(X0) [cnf transformation 60]
114. happy(X0) | creative(X0) [cnf transformation 62]
118. ~quiet(alice) [cnf transformation 18]
126. ~humble(mary) [cnf transformation 23]
173. 11 <=> happy(alice) [avatar definition]
174. ~happy(alice) <- (~11) [avatar component clause 173]
182. 13 <=> ! [X1] : brave(X1) [avatar definition]
183. brave(X1) <- (13) [avatar component clause 182]
184. 13 | ~11 [avatar split clause 80,173,182]
213. 19 <=> strong(alice) [avatar definition]
214. strong(alice) <- (19) [avatar component clause 213]
257. humble(X0) <- (13) [resolution 106,183]
259. $false <- (13) [resolution 257,126]
260. ~13 [avatar contradiction clause 259]
266. creative(alice) <- (~11) [resolution 114,174]
268. strong(alice) <- (~11) [resolution 266,82]
271. 19 | 11 [avatar split clause 268,173,213]
272. quiet(alice) <- (19) [resolution 214,111]
274. $false <- (19) [subsumption resolution 272,118]
275. ~19 [avatar contradiction clause 274]
276. $false [avatar sat refutation 184,260,271,275]
% SZS output end Proof for 6674803765604290338976318
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is old or creative is both strong and not rich.
If fred is not curious then alice is either not brave or curious and vice versa.
Everyone who is not kind or not calm is patient.
Everyone who is not patient is happy or funny.
Everyone who is not calm or creative is old or patient.
If someone is humble then lucy is rich and vice versa.
If someone is both not humble and rich then someone is both curious and quiet and vice versa.
Everyone who is kind or calm is not strong or not calm and vice versa.
If someone is either not patient or not calm then fred is either curious or brave and vice versa.
Everyone who is either not creative or not quiet is not old and vice versa.
Everyone who is either not tall or old is either not wise or not creative and vice versa.
Everyone who is not old is both old and not creative and vice versa.
Everyone who is not wise is both not humble and patient and vice versa.
If someone is not rich or not happy then mary is kind or generous.
Everyone who is not patient is calm and vice versa.
Paul is both not happy and not rich.
Someone is both not happy and kind.
Someone is rich or not humble.
Mary is both old and generous. | Alice is tall. | entailment | (![X]:((old(X)|creative(X))=>(strong(X)&~rich(X))))&
((~curious(fred))<=>((~brave(alice)<~>curious(alice))))&
(![X]:((~kind(X)|~calm(X))=>patient(X)))&
(![X]:(~patient(X)=>(happy(X)|funny(X))))&
(![X]:((~calm(X)|creative(X))=>(old(X)|patient(X))))&
((?[X]:(humble(X)))<=>(rich(lucy)))&
((?[X]:((~humble(X)&rich(X))))<=>(?[X]:((curious(X)&quiet(X)))))&
(![X]:((kind(X)|calm(X))<=>(~strong(X)|~calm(X))))&
((?[X]:((~patient(X)<~>~calm(X))))<=>((curious(fred)<~>brave(fred))))&
(![X]:((~creative(X)<~>~quiet(X))<=>~old(X)))&
(![X]:((~tall(X)<~>old(X))<=>(~wise(X)<~>~creative(X))))&
(![X]:(~old(X)<=>(old(X)&~creative(X))))&
(![X]:(~wise(X)<=>(~humble(X)&patient(X))))&
((?[X]:((~rich(X)|~happy(X))))=>((kind(mary)|generous(mary))))&
(![X]:(~patient(X)<=>calm(X)))&
((~happy(paul)&~rich(paul)))&
(?[X]:((~happy(X)&kind(X))))&
(?[X]:((rich(X)|~humble(X))))&
((old(mary)&generous(mary))) | tall(alice) | [
"p0",
"p2",
"p5",
"p7",
"p10",
"p11",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 3499377352023313094366115
% SZS output start Proof for 3499377352023313094366115
1. ! [X0] : ((creative(X0) | old(X0)) => (~rich(X0) & strong(X0))) [input p0]
3. ! [X0] : ((~calm(X0) | ~kind(X0)) => patient(X0)) [input p2]
6. ? [X0] : humble(X0) <=> rich(lucy) [input p5]
8. ! [X0] : ((calm(X0) | kind(X0)) <=> (~calm(X0) | ~strong(X0))) [input p7]
11. ! [X0] : ((~tall(X0) <~> old(X0)) <=> (~wise(X0) <~> ~creative(X0))) [input p10]
12. ! [X0] : (~old(X0) <=> (~creative(X0) & old(X0))) [input p11]
13. ! [X0] : (~wise(X0) <=> (patient(X0) & ~humble(X0))) [input p12]
20. ~tall(alice) [input hypothesis]
27. ! [X0] : ((~rich(X0) & strong(X0)) | (~creative(X0) & ~old(X0))) [ennf transformation 1]
28. ! [X0] : (patient(X0) | (calm(X0) & kind(X0))) [ennf transformation 3]
32. (? [X0] : humble(X0) | ~rich(lucy)) & (rich(lucy) | ! [X0] : ~humble(X0)) [nnf transformation 6]
33. (? [X0] : humble(X0) | ~rich(lucy)) & (rich(lucy) | ! [X1] : ~humble(X1)) [rectify 32]
34. ? [X0] : humble(X0) => humble(sK0) [choice axiom]
35. (humble(sK0) | ~rich(lucy)) & (rich(lucy) | ! [X1] : ~humble(X1)) [skolemisation 33,34]
41. ! [X0] : (((calm(X0) | kind(X0)) | (calm(X0) & strong(X0))) & ((~calm(X0) | ~strong(X0)) | (~calm(X0) & ~kind(X0)))) [nnf transformation 8]
42. ! [X0] : ((calm(X0) | kind(X0) | (calm(X0) & strong(X0))) & (~calm(X0) | ~strong(X0) | (~calm(X0) & ~kind(X0)))) [flattening 41]
48. ! [X0] : ((((~old(X0) | tall(X0)) & (old(X0) | ~tall(X0))) | ((~wise(X0) | creative(X0)) & (~creative(X0) | wise(X0)))) & (((creative(X0) | wise(X0)) & (~creative(X0) | ~wise(X0))) | ((~tall(X0) | ~old(X0)) & (old(X0) | tall(X0))))) [nnf transformation 11]
49. ! [X0] : ((~old(X0) | (creative(X0) | ~old(X0))) & ((~creative(X0) & old(X0)) | old(X0))) [nnf transformation 12]
50. ! [X0] : ((~old(X0) | creative(X0) | ~old(X0)) & ((~creative(X0) & old(X0)) | old(X0))) [flattening 49]
51. ! [X0] : ((~wise(X0) | (~patient(X0) | humble(X0))) & ((patient(X0) & ~humble(X0)) | wise(X0))) [nnf transformation 13]
52. ! [X0] : ((~wise(X0) | ~patient(X0) | humble(X0)) & ((patient(X0) & ~humble(X0)) | wise(X0))) [flattening 51]
58. ~old(X0) | strong(X0) [cnf transformation 27]
60. ~rich(X0) | ~old(X0) [cnf transformation 27]
67. patient(X0) | calm(X0) [cnf transformation 28]
70. rich(lucy) | ~humble(X1) [cnf transformation 35]
77. ~calm(X0) | ~strong(X0) | ~calm(X0) [cnf transformation 42]
98. ~creative(X0) | tall(X0) | ~old(X0) | wise(X0) [cnf transformation 48]
100. old(X0) | old(X0) [cnf transformation 50]
102. ~old(X0) | creative(X0) | ~old(X0) [cnf transformation 50]
105. ~wise(X0) | ~patient(X0) | humble(X0) [cnf transformation 52]
112. ~tall(alice) [cnf transformation 20]
113. old(X0) [duplicate literal removal 100]
114. ~old(X0) | creative(X0) [duplicate literal removal 102]
115. ~calm(X0) | ~strong(X0) [duplicate literal removal 77]
134. 4 <=> rich(lucy) [avatar definition]
135. rich(lucy) <- (4) [avatar component clause 134]
143. 6 <=> ! [X1] : ~humble(X1) [avatar definition]
144. ~humble(X1) <- (6) [avatar component clause 143]
145. 6 | 4 [avatar split clause 70,134,143]
209. strong(X0) [resolution 58,113]
210. ~old(lucy) <- (4) [resolution 60,135]
211. $false <- (4) [subsumption resolution 210,113]
212. ~4 [avatar contradiction clause 211]
218. creative(X0) [resolution 114,113]
258. tall(X0) | ~old(X0) | wise(X0) [resolution 98,218]
259. wise(X0) | tall(X0) [subsumption resolution 258,113]
267. tall(X4) | ~patient(X4) | humble(X4) [resolution 259,105]
270. ~patient(X4) | tall(X4) <- (6) [subsumption resolution 267,144]
271. tall(X0) | calm(X0) <- (6) [resolution 270,67]
273. calm(alice) <- (6) [resolution 271,112]
277. ~strong(alice) <- (6) [resolution 273,115]
278. $false <- (6) [subsumption resolution 277,209]
279. ~6 [avatar contradiction clause 278]
280. $false [avatar sat refutation 145,212,279]
% SZS output end Proof for 3499377352023313094366115
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either funny or happy then someone is either patient or not patient. If someone is both not brave and rich then susan is either not wise or strong and vice versa. Everyone who is either not brave or kind is not strong. If someone is not quiet then alice is both wise and kind. If alice is either not quiet or funny then someone is either not kind or creative. Everyone who is not brave is both not strong and not wise. If someone is tall or not tall then someone is not curious or not strong. Everyone who is not quiet or quiet is both kind and not brave and vice versa. Everyone who is both patient and not strong is both generous and not strong. If someone is either quiet or curious then someone is both curious and rich and vice versa. If someone is not curious then mary is tall and vice versa. Everyone who is generous is not happy and vice versa. If alice is patient then lucy is quiet and vice versa. If lucy is either patient or calm then paul is calm and vice versa. If alice is both not happy and quiet then lucy is both creative and calm. John is either not happy or calm. Mary is either calm or curious. Someone is both not strong and old. Someone is happy. Someone is curious or not curious. | Susan is wise. | contradiction | ((?[X]:((funny(X)<~>happy(X))))=>(?[X]:((patient(X)<~>~patient(X)))))&
((?[X]:((~brave(X)&rich(X))))<=>((~wise(susan)<~>strong(susan))))&
(![X]:((~brave(X)<~>kind(X))=>~strong(X)))&
((?[X]:(~quiet(X)))=>((wise(alice)&kind(alice))))&
(((~quiet(alice)<~>funny(alice)))=>(?[X]:((~kind(X)<~>creative(X)))))&
(![X]:(~brave(X)=>(~strong(X)&~wise(X))))&
((?[X]:((tall(X)|~tall(X))))=>(?[X]:((~curious(X)|~strong(X)))))&
(![X]:((~quiet(X)|quiet(X))<=>(kind(X)&~brave(X))))&
(![X]:((patient(X)&~strong(X))=>(generous(X)&~strong(X))))&
((?[X]:((quiet(X)<~>curious(X))))<=>(?[X]:((curious(X)&rich(X)))))&
((?[X]:(~curious(X)))<=>(tall(mary)))&
(![X]:(generous(X)<=>~happy(X)))&
((patient(alice))<=>(quiet(lucy)))&
(((patient(lucy)<~>calm(lucy)))<=>(calm(paul)))&
(((~happy(alice)&quiet(alice)))=>((creative(lucy)&calm(lucy))))&
((~happy(john)<~>calm(john)))&
((calm(mary)<~>curious(mary)))&
(?[X]:((~strong(X)&old(X))))&
(?[X]:(happy(X)))&
(?[X]:((curious(X)|~curious(X)))) | wise(susan) | [
"p5",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 8903371787892541943405535
% SZS output start Proof for 8903371787892541943405535
6. ! [X0] : (~brave(X0) => (~wise(X0) & ~strong(X0))) [input p5]
8. ! [X0] : ((quiet(X0) | ~quiet(X0)) <=> (~brave(X0) & kind(X0))) [input p7]
21. wise(susan) [input hypothesis]
31. ! [X0] : ((~wise(X0) & ~strong(X0)) | brave(X0)) [ennf transformation 6]
53. ! [X0] : (((quiet(X0) | ~quiet(X0)) | (brave(X0) | ~kind(X0))) & ((~brave(X0) & kind(X0)) | (~quiet(X0) & quiet(X0)))) [nnf transformation 8]
54. ! [X0] : ((quiet(X0) | ~quiet(X0) | brave(X0) | ~kind(X0)) & ((~brave(X0) & kind(X0)) | (~quiet(X0) & quiet(X0)))) [flattening 53]
93. ~wise(X0) | brave(X0) [cnf transformation 31]
98. ~brave(X0) | quiet(X0) [cnf transformation 54]
99. ~brave(X0) | ~quiet(X0) [cnf transformation 54]
127. wise(susan) [cnf transformation 21]
133. 2 <=> wise(susan) [avatar definition]
134. wise(susan) <- (2) [avatar component clause 133]
202. ~brave(X0) [subsumption resolution 98,99]
304. 2 [avatar split clause 127,133]
310. brave(susan) <- (2) [resolution 93,134]
312. $false <- (2) [subsumption resolution 310,202]
313. ~2 [avatar contradiction clause 312]
316. $false [avatar sat refutation 304,313]
% SZS output end Proof for 8903371787892541943405535
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not rich is creative.
Everyone who is either tall or funny is not generous.
Everyone who is quiet is both patient and not rich and vice versa.
Everyone who is either quiet or not old is strong or not humble.
Everyone who is patient or curious is both curious and strong and vice versa.
Everyone who is not kind or not patient is not humble and vice versa.
Everyone who is not calm is not creative or wise.
If someone is either not calm or creative then susan is both tall and not humble.
Everyone who is either not creative or not funny is not strong.
If someone is both curious and not creative then fred is curious or not funny and vice versa.
Everyone who is patient or not rich is not creative.
Everyone who is rich is quiet or patient and vice versa.
Everyone who is both not old and not patient is both wise and not brave and vice versa.
If someone is not patient then someone is generous or not patient and vice versa.
If someone is either kind or not funny then someone is both patient and rich and vice versa.
If lucy is both not patient and patient then mary is not strong and vice versa.
Mary is either not calm or not curious.
Someone is both not old and not happy.
Mary is humble.
Someone is not happy.
Someone is either not tall or patient.
Alice is creative or tall.
Someone is kind or not funny. | Lucy is not patient. | contradiction | (![X]:(~rich(X)=>creative(X)))&
(![X]:((tall(X)<~>funny(X))=>~generous(X)))&
(![X]:(quiet(X)<=>(patient(X)&~rich(X))))&
(![X]:((quiet(X)<~>~old(X))=>(strong(X)|~humble(X))))&
(![X]:((patient(X)|curious(X))<=>(curious(X)&strong(X))))&
(![X]:((~kind(X)|~patient(X))<=>~humble(X)))&
(![X]:(~calm(X)=>(~creative(X)|wise(X))))&
((?[X]:((~calm(X)<~>creative(X))))=>((tall(susan)&~humble(susan))))&
(![X]:((~creative(X)<~>~funny(X))=>~strong(X)))&
((?[X]:((curious(X)&~creative(X))))<=>((curious(fred)|~funny(fred))))&
(![X]:((patient(X)|~rich(X))=>~creative(X)))&
(![X]:(rich(X)<=>(quiet(X)|patient(X))))&
(![X]:((~old(X)&~patient(X))<=>(wise(X)&~brave(X))))&
((?[X]:(~patient(X)))<=>(?[X]:((generous(X)|~patient(X)))))&
((?[X]:((kind(X)<~>~funny(X))))<=>(?[X]:((patient(X)&rich(X)))))&
(((~patient(lucy)&patient(lucy)))<=>(~strong(mary)))&
((~calm(mary)<~>~curious(mary)))&
(?[X]:((~old(X)&~happy(X))))&
(humble(mary))&
(?[X]:(~happy(X)))&
(?[X]:((~tall(X)<~>patient(X))))&
((creative(alice)|tall(alice)))&
(?[X]:((kind(X)|~funny(X)))) | ~patient(lucy) | [
"p0",
"p2",
"p10",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 8379847549591372300526621
% SZS output start Proof for 8379847549591372300526621
1. ! [X0] : (~rich(X0) => creative(X0)) [input p0]
3. ! [X0] : (quiet(X0) <=> (~rich(X0) & patient(X0))) [input p2]
11. ! [X0] : ((~rich(X0) | patient(X0)) => ~creative(X0)) [input p10]
12. ! [X0] : (rich(X0) <=> (patient(X0) | quiet(X0))) [input p11]
24. ~patient(lucy) [input hypothesis]
29. ! [X0] : (creative(X0) | rich(X0)) [ennf transformation 1]
37. ! [X0] : (~creative(X0) | (rich(X0) & ~patient(X0))) [ennf transformation 11]
39. ! [X0] : ((quiet(X0) | (rich(X0) | ~patient(X0))) & ((~rich(X0) & patient(X0)) | ~quiet(X0))) [nnf transformation 3]
40. ! [X0] : ((quiet(X0) | rich(X0) | ~patient(X0)) & ((~rich(X0) & patient(X0)) | ~quiet(X0))) [flattening 39]
53. ! [X0] : ((rich(X0) | (~patient(X0) & ~quiet(X0))) & ((patient(X0) | quiet(X0)) | ~rich(X0))) [nnf transformation 12]
54. ! [X0] : ((rich(X0) | (~patient(X0) & ~quiet(X0))) & (patient(X0) | quiet(X0) | ~rich(X0))) [flattening 53]
77. creative(X0) | rich(X0) [cnf transformation 29]
80. patient(X0) | ~quiet(X0) [cnf transformation 40]
106. ~creative(X0) | rich(X0) [cnf transformation 37]
107. patient(X0) | quiet(X0) | ~rich(X0) [cnf transformation 54]
134. ~patient(lucy) [cnf transformation 24]
177. rich(X0) [subsumption resolution 106,77]
178. patient(X0) | quiet(X0) [subsumption resolution 107,177]
179. patient(X0) [subsumption resolution 178,80]
226. $false [subsumption resolution 134,179]
% SZS output end Proof for 8379847549591372300526621
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is either wise or calm then paul is quiet and vice versa. If susan is not wise then someone is not happy or patient and vice versa. Everyone who is not strong or brave is generous or curious. If someone is both not generous and creative then mary is both not strong and not curious. If paul is not funny then someone is calm and vice versa. Everyone who is strong is not happy or humble and vice versa. Everyone who is not quiet or not humble is tall or patient and vice versa. If someone is not wise or brave then fred is either not humble or not brave and vice versa. Everyone who is either not generous or creative is both humble and not funny and vice versa. If someone is both generous and not wise then mary is wise or curious and vice versa. Everyone who is either not patient or humble is not brave. Everyone who is curious is not wise and vice versa. Everyone who is either not wise or not happy is both humble and kind and vice versa. Everyone who is old or kind is both not creative and strong and vice versa. Everyone who is either creative or kind is both curious and not generous and vice versa. Everyone who is either tall or not humble is either brave or not calm and vice versa. Someone is both strong and funny. Mary is happy. Someone is rich. Someone is both creative and not patient. John is either not kind or happy. Fred is not patient or not creative. Susan is both not happy and not wise. | John is not curious. | contradiction | (((wise(lucy)<~>calm(lucy)))<=>(quiet(paul)))&
((~wise(susan))<=>(?[X]:((~happy(X)|patient(X)))))&
(![X]:((~strong(X)|brave(X))=>(generous(X)|curious(X))))&
((?[X]:((~generous(X)&creative(X))))=>((~strong(mary)&~curious(mary))))&
((~funny(paul))<=>(?[X]:(calm(X))))&
(![X]:(strong(X)<=>(~happy(X)|humble(X))))&
(![X]:((~quiet(X)|~humble(X))<=>(tall(X)|patient(X))))&
((?[X]:((~wise(X)|brave(X))))<=>((~humble(fred)<~>~brave(fred))))&
(![X]:((~generous(X)<~>creative(X))<=>(humble(X)&~funny(X))))&
((?[X]:((generous(X)&~wise(X))))<=>((wise(mary)|curious(mary))))&
(![X]:((~patient(X)<~>humble(X))=>~brave(X)))&
(![X]:(curious(X)<=>~wise(X)))&
(![X]:((~wise(X)<~>~happy(X))<=>(humble(X)&kind(X))))&
(![X]:((old(X)|kind(X))<=>(~creative(X)&strong(X))))&
(![X]:((creative(X)<~>kind(X))<=>(curious(X)&~generous(X))))&
(![X]:((tall(X)<~>~humble(X))<=>(brave(X)<~>~calm(X))))&
(?[X]:((strong(X)&funny(X))))&
(happy(mary))&
(?[X]:(rich(X)))&
(?[X]:((creative(X)&~patient(X))))&
((~kind(john)<~>happy(john)))&
((~patient(fred)|~creative(fred)))&
((~happy(susan)&~wise(susan))) | ~curious(john) | [
"p11",
"p12",
"p13",
"p14",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 9128038767016830183467650
% SZS output start Proof for 9128038767016830183467650
12. ! [X0] : (curious(X0) <=> ~wise(X0)) [input p11]
13. ! [X0] : ((~wise(X0) <~> ~happy(X0)) <=> (kind(X0) & humble(X0))) [input p12]
14. ! [X0] : ((kind(X0) | old(X0)) <=> (strong(X0) & ~creative(X0))) [input p13]
15. ! [X0] : ((creative(X0) <~> kind(X0)) <=> (~generous(X0) & curious(X0))) [input p14]
21. ~kind(john) <~> happy(john) [input p20]
24. ~curious(john) [input hypothesis]
55. ! [X0] : ((curious(X0) | wise(X0)) & (~wise(X0) | ~curious(X0))) [nnf transformation 12]
56. ! [X0] : ((((happy(X0) | wise(X0)) & (~happy(X0) | ~wise(X0))) | (~kind(X0) | ~humble(X0))) & ((kind(X0) & humble(X0)) | ((~wise(X0) | happy(X0)) & (~happy(X0) | wise(X0))))) [nnf transformation 13]
57. ! [X0] : ((((happy(X0) | wise(X0)) & (~happy(X0) | ~wise(X0))) | ~kind(X0) | ~humble(X0)) & ((kind(X0) & humble(X0)) | ((~wise(X0) | happy(X0)) & (~happy(X0) | wise(X0))))) [flattening 56]
58. ! [X0] : (((kind(X0) | old(X0)) | (~strong(X0) | creative(X0))) & ((strong(X0) & ~creative(X0)) | (~kind(X0) & ~old(X0)))) [nnf transformation 14]
59. ! [X0] : ((kind(X0) | old(X0) | ~strong(X0) | creative(X0)) & ((strong(X0) & ~creative(X0)) | (~kind(X0) & ~old(X0)))) [flattening 58]
60. ! [X0] : ((((~kind(X0) | ~creative(X0)) & (kind(X0) | creative(X0))) | (generous(X0) | ~curious(X0))) & ((~generous(X0) & curious(X0)) | ((creative(X0) | ~kind(X0)) & (kind(X0) | ~creative(X0))))) [nnf transformation 15]
61. ! [X0] : ((((~kind(X0) | ~creative(X0)) & (kind(X0) | creative(X0))) | generous(X0) | ~curious(X0)) & ((~generous(X0) & curious(X0)) | ((creative(X0) | ~kind(X0)) & (kind(X0) | ~creative(X0))))) [flattening 60]
67. (~happy(john) | kind(john)) & (happy(john) | ~kind(john)) [nnf transformation 21]
108. curious(X0) | wise(X0) [cnf transformation 55]
112. ~wise(X0) | kind(X0) | happy(X0) [cnf transformation 57]
116. ~kind(X0) | ~creative(X0) [cnf transformation 59]
121. curious(X0) | creative(X0) | ~kind(X0) [cnf transformation 61]
140. ~happy(john) | kind(john) [cnf transformation 67]
144. ~curious(john) [cnf transformation 24]
258. ~kind(X0) | curious(X0) [subsumption resolution 121,116]
261. 25 <=> kind(john) [avatar definition]
263. kind(john) <- (25) [avatar component clause 261]
265. 26 <=> happy(john) [avatar definition]
268. 25 | ~26 [avatar split clause 140,265,261]
284. wise(john) [resolution 108,144]
385. kind(john) | happy(john) [resolution 112,284]
389. 26 | 25 [avatar split clause 385,261,265]
396. curious(john) <- (25) [resolution 263,258]
400. $false <- (25) [subsumption resolution 396,144]
401. ~25 [avatar contradiction clause 400]
406. $false [avatar sat refutation 268,389,401]
% SZS output end Proof for 9128038767016830183467650
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.029 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not calm and not brave then someone is creative or curious and vice versa.
Everyone who is either quiet or humble is either strong or not humble and vice versa.
If lucy is both not funny and generous then fred is both not generous and not happy and vice versa.
If lucy is both not rich and curious then mary is not kind.
If someone is brave or kind then someone is not humble or not calm.
Everyone who is either happy or not brave is either not wise or curious and vice versa.
Everyone who is either not generous or not humble is both not rich and patient.
If someone is not calm then someone is either not happy or not brave.
If someone is not humble then lucy is both not calm and tall.
Everyone who is not happy or not kind is not creative and vice versa.
If fred is kind or generous then lucy is rich and vice versa.
Everyone who is both not old and old is happy or kind.
Everyone who is both funny and quiet is curious and vice versa.
If someone is either generous or brave then mary is not calm and vice versa.
Everyone who is either not curious or strong is not creative or old.
If mary is both rich and strong then someone is creative or not rich and vice versa.
Someone is either strong or tall.
Someone is brave.
Someone is either not curious or not calm.
Mary is not strong or creative.
Fred is calm.
Someone is either not generous or not funny.
Someone is not brave or kind.
Mary is both quiet and not happy. | Fred is not brave. | neutral | ((?[X]:((~calm(X)&~brave(X))))<=>(?[X]:((creative(X)|curious(X)))))&
(![X]:((quiet(X)<~>humble(X))<=>(strong(X)<~>~humble(X))))&
(((~funny(lucy)&generous(lucy)))<=>((~generous(fred)&~happy(fred))))&
(((~rich(lucy)&curious(lucy)))=>(~kind(mary)))&
((?[X]:((brave(X)|kind(X))))=>(?[X]:((~humble(X)|~calm(X)))))&
(![X]:((happy(X)<~>~brave(X))<=>(~wise(X)<~>curious(X))))&
(![X]:((~generous(X)<~>~humble(X))=>(~rich(X)&patient(X))))&
((?[X]:(~calm(X)))=>(?[X]:((~happy(X)<~>~brave(X)))))&
((?[X]:(~humble(X)))=>((~calm(lucy)&tall(lucy))))&
(![X]:((~happy(X)|~kind(X))<=>~creative(X)))&
(((kind(fred)|generous(fred)))<=>(rich(lucy)))&
(![X]:((~old(X)&old(X))=>(happy(X)|kind(X))))&
(![X]:((funny(X)&quiet(X))<=>curious(X)))&
((?[X]:((generous(X)<~>brave(X))))<=>(~calm(mary)))&
(![X]:((~curious(X)<~>strong(X))=>(~creative(X)|old(X))))&
(((rich(mary)&strong(mary)))<=>(?[X]:((creative(X)|~rich(X)))))&
(?[X]:((strong(X)<~>tall(X))))&
(?[X]:(brave(X)))&
(?[X]:((~curious(X)<~>~calm(X))))&
((~strong(mary)|creative(mary)))&
(calm(fred))&
(?[X]:((~generous(X)<~>~funny(X))))&
(?[X]:((~brave(X)|kind(X))))&
((quiet(mary)&~happy(mary))) | ~brave(fred) | [] | null | 0 |
Everyone who is either not brave or not generous is both not brave and not tall and vice versa.
If someone is not wise or humble then mary is patient or strong.
If lucy is curious then someone is not brave and vice versa.
Everyone who is not old or not brave is either happy or not old.
Everyone who is curious or tall is calm.
If someone is both tall and not curious then paul is not brave or not creative.
Everyone who is quiet or funny is old or not old.
If mary is both not wise and happy then alice is either humble or not happy.
If john is either strong or not humble then john is both brave and not wise.
Everyone who is not funny or not wise is both strong and not wise.
Everyone who is both not curious and tall is both brave and not wise and vice versa.
Everyone who is both not tall and tall is not wise or not calm and vice versa.
Everyone who is generous or not strong is either not brave or not funny and vice versa.
Everyone who is rich is not happy or not generous and vice versa.
If fred is either not quiet or quiet then alice is not tall and vice versa.
Everyone who is both not wise and curious is both not quiet and not old.
Someone is both not happy and not tall.
Susan is strong or not old.
Someone is either not curious or not patient.
Lucy is wise.
Fred is either not curious or not funny.
Paul is not curious. | Paul is tall. | contradiction | (![X]:((~brave(X)<~>~generous(X))<=>(~brave(X)&~tall(X))))&
((?[X]:((~wise(X)|humble(X))))=>((patient(mary)|strong(mary))))&
((curious(lucy))<=>(?[X]:(~brave(X))))&
(![X]:((~old(X)|~brave(X))=>(happy(X)<~>~old(X))))&
(![X]:((curious(X)|tall(X))=>calm(X)))&
((?[X]:((tall(X)&~curious(X))))=>((~brave(paul)|~creative(paul))))&
(![X]:((quiet(X)|funny(X))=>(old(X)|~old(X))))&
(((~wise(mary)&happy(mary)))=>((humble(alice)<~>~happy(alice))))&
(((strong(john)<~>~humble(john)))=>((brave(john)&~wise(john))))&
(![X]:((~funny(X)|~wise(X))=>(strong(X)&~wise(X))))&
(![X]:((~curious(X)&tall(X))<=>(brave(X)&~wise(X))))&
(![X]:((~tall(X)&tall(X))<=>(~wise(X)|~calm(X))))&
(![X]:((generous(X)|~strong(X))<=>(~brave(X)<~>~funny(X))))&
(![X]:(rich(X)<=>(~happy(X)|~generous(X))))&
(((~quiet(fred)<~>quiet(fred)))<=>(~tall(alice)))&
(![X]:((~wise(X)&curious(X))=>(~quiet(X)&~old(X))))&
(?[X]:((~happy(X)&~tall(X))))&
((strong(susan)|~old(susan)))&
(?[X]:((~curious(X)<~>~patient(X))))&
(wise(lucy))&
((~curious(fred)<~>~funny(fred)))&
(~curious(paul)) | tall(paul) | [
"p0",
"p9",
"p10",
"p11",
"p12",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 6267654882893338957657081
% SZS output start Proof for 6267654882893338957657081
1. ! [X0] : ((~brave(X0) <~> ~generous(X0)) <=> (~tall(X0) & ~brave(X0))) [input p0]
10. ! [X0] : ((~wise(X0) | ~funny(X0)) => (~wise(X0) & strong(X0))) [input p9]
11. ! [X0] : ((tall(X0) & ~curious(X0)) <=> (~wise(X0) & brave(X0))) [input p10]
12. ! [X0] : ((tall(X0) & ~tall(X0)) <=> (~calm(X0) | ~wise(X0))) [input p11]
13. ! [X0] : ((~strong(X0) | generous(X0)) <=> (~brave(X0) <~> ~funny(X0))) [input p12]
22. ~curious(paul) [input p21]
23. tall(paul) [input hypothesis]
34. ! [X0] : ((~wise(X0) & strong(X0)) | (wise(X0) & funny(X0))) [ennf transformation 10]
37. ! [X0] : ((((generous(X0) | brave(X0)) & (~generous(X0) | ~brave(X0))) | (tall(X0) | brave(X0))) & ((~tall(X0) & ~brave(X0)) | ((~brave(X0) | generous(X0)) & (~generous(X0) | brave(X0))))) [nnf transformation 1]
38. ! [X0] : ((((generous(X0) | brave(X0)) & (~generous(X0) | ~brave(X0))) | tall(X0) | brave(X0)) & ((~tall(X0) & ~brave(X0)) | ((~brave(X0) | generous(X0)) & (~generous(X0) | brave(X0))))) [flattening 37]
46. ! [X0] : (((tall(X0) & ~curious(X0)) | (wise(X0) | ~brave(X0))) & ((~wise(X0) & brave(X0)) | (~tall(X0) | curious(X0)))) [nnf transformation 11]
47. ! [X0] : (((tall(X0) & ~curious(X0)) | wise(X0) | ~brave(X0)) & ((~wise(X0) & brave(X0)) | ~tall(X0) | curious(X0))) [flattening 46]
48. ! [X0] : (((tall(X0) & ~tall(X0)) | (calm(X0) & wise(X0))) & ((~calm(X0) | ~wise(X0)) | (~tall(X0) | tall(X0)))) [nnf transformation 12]
49. ! [X0] : (((tall(X0) & ~tall(X0)) | (calm(X0) & wise(X0))) & (~calm(X0) | ~wise(X0) | ~tall(X0) | tall(X0))) [flattening 48]
50. ! [X0] : (((~strong(X0) | generous(X0)) | ((~brave(X0) | funny(X0)) & (~funny(X0) | brave(X0)))) & (((funny(X0) | brave(X0)) & (~funny(X0) | ~brave(X0))) | (strong(X0) & ~generous(X0)))) [nnf transformation 13]
51. ! [X0] : ((~strong(X0) | generous(X0) | ((~brave(X0) | funny(X0)) & (~funny(X0) | brave(X0)))) & (((funny(X0) | brave(X0)) & (~funny(X0) | ~brave(X0))) | (strong(X0) & ~generous(X0)))) [flattening 50]
60. ~brave(X0) | ~brave(X0) | generous(X0) [cnf transformation 38]
85. ~wise(X0) | funny(X0) [cnf transformation 34]
87. ~tall(X0) | brave(X0) | curious(X0) [cnf transformation 47]
92. ~tall(X0) | wise(X0) [cnf transformation 49]
94. wise(X0) | tall(X0) [cnf transformation 49]
96. ~funny(X0) | ~brave(X0) | ~generous(X0) [cnf transformation 51]
116. ~curious(paul) [cnf transformation 22]
117. tall(paul) [cnf transformation 23]
121. ~brave(X0) | generous(X0) [duplicate literal removal 60]
136. 4 <=> ! [X0] : wise(X0) [avatar definition]
137. wise(X0) <- (4) [avatar component clause 136]
191. wise(X0) [subsumption resolution 92,94]
192. 4 [avatar split clause 191,136]
195. ~funny(X0) | ~brave(X0) [subsumption resolution 96,121]
244. funny(X0) <- (4) [resolution 85,137]
248. ~brave(X0) <- (4) [resolution 195,244]
254. brave(paul) | curious(paul) [resolution 87,117]
255. curious(paul) <- (4) [subsumption resolution 254,248]
256. $false <- (4) [subsumption resolution 255,116]
257. ~4 [avatar contradiction clause 256]
258. $false [avatar sat refutation 192,257]
% SZS output end Proof for 6267654882893338957657081
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is wise or not generous is quiet and vice versa.
If fred is both creative and not old then someone is not quiet or kind and vice versa.
Everyone who is both not tall and creative is either creative or not happy and vice versa.
Everyone who is not generous is both not patient and not brave.
Everyone who is either not kind or not patient is not calm or tall and vice versa.
Everyone who is creative is both not rich and not patient.
Everyone who is happy is funny or not funny and vice versa.
If susan is either creative or not happy then fred is not quiet and vice versa.
Everyone who is both calm and not quiet is not funny.
If alice is either funny or not happy then alice is both not brave and generous and vice versa.
If someone is not patient or wise then susan is both not funny and rich and vice versa.
Everyone who is either not kind or calm is either patient or funny and vice versa.
If fred is both humble and kind then someone is not creative or humble.
If someone is both rich and not tall then someone is curious or not patient.
Someone is either not rich or not strong.
John is not curious or not wise.
Alice is humble or not tall.
Lucy is either not generous or old.
Someone is both not quiet and not old.
John is both not patient and not creative.
Someone is not kind. | Fred is not rich. | entailment | (![X]:((wise(X)|~generous(X))<=>quiet(X)))&
(((creative(fred)&~old(fred)))<=>(?[X]:((~quiet(X)|kind(X)))))&
(![X]:((~tall(X)&creative(X))<=>(creative(X)<~>~happy(X))))&
(![X]:(~generous(X)=>(~patient(X)&~brave(X))))&
(![X]:((~kind(X)<~>~patient(X))<=>(~calm(X)|tall(X))))&
(![X]:(creative(X)=>(~rich(X)&~patient(X))))&
(![X]:(happy(X)<=>(funny(X)|~funny(X))))&
(((creative(susan)<~>~happy(susan)))<=>(~quiet(fred)))&
(![X]:((calm(X)&~quiet(X))=>~funny(X)))&
(((funny(alice)<~>~happy(alice)))<=>((~brave(alice)&generous(alice))))&
((?[X]:((~patient(X)|wise(X))))<=>((~funny(susan)&rich(susan))))&
(![X]:((~kind(X)<~>calm(X))<=>(patient(X)<~>funny(X))))&
(((humble(fred)&kind(fred)))=>(?[X]:((~creative(X)|humble(X)))))&
((?[X]:((rich(X)&~tall(X))))=>(?[X]:((curious(X)|~patient(X)))))&
(?[X]:((~rich(X)<~>~strong(X))))&
((~curious(john)|~wise(john)))&
((humble(alice)|~tall(alice)))&
((~generous(lucy)<~>old(lucy)))&
(?[X]:((~quiet(X)&~old(X))))&
((~patient(john)&~creative(john)))&
(?[X]:(~kind(X))) | ~rich(fred) | [
"p1",
"p5",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 2418409495999368962756450
% SZS output start Proof for 2418409495999368962756450
2. (~old(fred) & creative(fred)) <=> ? [X0] : (kind(X0) | ~quiet(X0)) [input p1]
6. ! [X0] : (creative(X0) => (~patient(X0) & ~rich(X0))) [input p5]
19. ? [X0] : (~old(X0) & ~quiet(X0)) [input p18]
22. rich(fred) [input hypothesis]
25. ! [X0] : ((~patient(X0) & ~rich(X0)) | ~creative(X0)) [ennf transformation 6]
33. ((~old(fred) & creative(fred)) | ! [X0] : (~kind(X0) & quiet(X0))) & (? [X0] : (kind(X0) | ~quiet(X0)) | (old(fred) | ~creative(fred))) [nnf transformation 2]
34. ((~old(fred) & creative(fred)) | ! [X0] : (~kind(X0) & quiet(X0))) & (? [X0] : (kind(X0) | ~quiet(X0)) | old(fred) | ~creative(fred)) [flattening 33]
35. ((~old(fred) & creative(fred)) | ! [X0] : (~kind(X0) & quiet(X0))) & (? [X1] : (kind(X1) | ~quiet(X1)) | old(fred) | ~creative(fred)) [rectify 34]
36. ? [X1] : (kind(X1) | ~quiet(X1)) => (kind(sK0) | ~quiet(sK0)) [choice axiom]
37. ((~old(fred) & creative(fred)) | ! [X0] : (~kind(X0) & quiet(X0))) & ((kind(sK0) | ~quiet(sK0)) | old(fred) | ~creative(fred)) [skolemisation 35,36]
62. ? [X0] : (~old(X0) & ~quiet(X0)) => (~old(sK5) & ~quiet(sK5)) [choice axiom]
63. ~old(sK5) & ~quiet(sK5) [skolemisation 19,62]
70. creative(fred) | quiet(X0) [cnf transformation 37]
88. ~rich(X0) | ~creative(X0) [cnf transformation 25]
125. ~quiet(sK5) [cnf transformation 63]
130. rich(fred) [cnf transformation 22]
142. 3 <=> ! [X0] : quiet(X0) [avatar definition]
143. quiet(X0) <- (3) [avatar component clause 142]
146. 4 <=> creative(fred) [avatar definition]
150. 3 | 4 [avatar split clause 70,146,142]
292. ~creative(fred) [resolution 88,130]
297. ~4 [avatar split clause 292,146]
298. $false <- (3) [resolution 143,125]
301. ~3 [avatar contradiction clause 298]
302. $false [avatar sat refutation 150,297,301]
% SZS output end Proof for 2418409495999368962756450
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not wise and not brave is not quiet or not old and vice versa.
If lucy is either not strong or quiet then someone is either brave or not generous.
Everyone who is not creative or not strong is quiet and vice versa.
Everyone who is either not brave or strong is not calm.
If someone is either not kind or not patient then someone is either not strong or not patient.
Everyone who is not old or brave is either not tall or not strong and vice versa.
If fred is rich then someone is not quiet or brave.
Everyone who is either kind or not brave is both not quiet and wise and vice versa.
If fred is both funny and tall then someone is both not funny and not kind.
Everyone who is creative is both not strong and wise and vice versa.
Everyone who is either not tall or not happy is not patient or not rich and vice versa.
Everyone who is humble is either not calm or not creative.
Everyone who is not curious is not calm.
If fred is not calm then someone is either calm or not brave and vice versa.
Everyone who is either not rich or kind is both not funny and quiet.
Someone is not old or strong.
Someone is not strong.
Lucy is not creative.
Alice is either not strong or not curious.
Lucy is either not happy or funny.
Someone is rich.
Alice is both calm and humble. | Alice is not rich. | neutral | (![X]:((~wise(X)&~brave(X))<=>(~quiet(X)|~old(X))))&
(((~strong(lucy)<~>quiet(lucy)))=>(?[X]:((brave(X)<~>~generous(X)))))&
(![X]:((~creative(X)|~strong(X))<=>quiet(X)))&
(![X]:((~brave(X)<~>strong(X))=>~calm(X)))&
((?[X]:((~kind(X)<~>~patient(X))))=>(?[X]:((~strong(X)<~>~patient(X)))))&
(![X]:((~old(X)|brave(X))<=>(~tall(X)<~>~strong(X))))&
((rich(fred))=>(?[X]:((~quiet(X)|brave(X)))))&
(![X]:((kind(X)<~>~brave(X))<=>(~quiet(X)&wise(X))))&
(((funny(fred)&tall(fred)))=>(?[X]:((~funny(X)&~kind(X)))))&
(![X]:(creative(X)<=>(~strong(X)&wise(X))))&
(![X]:((~tall(X)<~>~happy(X))<=>(~patient(X)|~rich(X))))&
(![X]:(humble(X)=>(~calm(X)<~>~creative(X))))&
(![X]:(~curious(X)=>~calm(X)))&
((~calm(fred))<=>(?[X]:((calm(X)<~>~brave(X)))))&
(![X]:((~rich(X)<~>kind(X))=>(~funny(X)&quiet(X))))&
(?[X]:((~old(X)|strong(X))))&
(?[X]:(~strong(X)))&
(~creative(lucy))&
((~strong(alice)<~>~curious(alice)))&
((~happy(lucy)<~>funny(lucy)))&
(?[X]:(rich(X)))&
((calm(alice)&humble(alice))) | ~rich(alice) | [] | null | 0 |
Everyone who is either not happy or brave is calm and vice versa.
Everyone who is rich is both quiet and strong and vice versa.
If someone is not patient or old then lucy is both not quiet and patient and vice versa.
Everyone who is either not wise or not curious is patient and vice versa.
Everyone who is either not quiet or not happy is tall and vice versa.
If fred is both not creative and rich then someone is not humble or not kind and vice versa.
If someone is either happy or curious then someone is both happy and not patient.
Everyone who is either wise or brave is either not old or not rich and vice versa.
Everyone who is not strong or not curious is both calm and not funny and vice versa.
If someone is either humble or kind then susan is both not happy and kind.
Everyone who is either generous or happy is not generous and vice versa.
If lucy is not brave or not quiet then paul is both humble and not generous and vice versa.
If lucy is funny then someone is kind or not happy and vice versa.
Everyone who is either rich or not calm is old.
If john is either not humble or brave then someone is either not calm or not patient and vice versa.
If someone is both quiet and not patient then mary is both not curious and not rich.
Fred is both tall and not quiet.
Susan is both not quiet and not generous.
Someone is not old.
Alice is rich or not curious.
Susan is calm.
Alice is both not generous and calm. | Paul is not generous. | entailment | (![X]:((~happy(X)<~>brave(X))<=>calm(X)))&
(![X]:(rich(X)<=>(quiet(X)&strong(X))))&
((?[X]:((~patient(X)|old(X))))<=>((~quiet(lucy)&patient(lucy))))&
(![X]:((~wise(X)<~>~curious(X))<=>patient(X)))&
(![X]:((~quiet(X)<~>~happy(X))<=>tall(X)))&
(((~creative(fred)&rich(fred)))<=>(?[X]:((~humble(X)|~kind(X)))))&
((?[X]:((happy(X)<~>curious(X))))=>(?[X]:((happy(X)&~patient(X)))))&
(![X]:((wise(X)<~>brave(X))<=>(~old(X)<~>~rich(X))))&
(![X]:((~strong(X)|~curious(X))<=>(calm(X)&~funny(X))))&
((?[X]:((humble(X)<~>kind(X))))=>((~happy(susan)&kind(susan))))&
(![X]:((generous(X)<~>happy(X))<=>~generous(X)))&
(((~brave(lucy)|~quiet(lucy)))<=>((humble(paul)&~generous(paul))))&
((funny(lucy))<=>(?[X]:((kind(X)|~happy(X)))))&
(![X]:((rich(X)<~>~calm(X))=>old(X)))&
(((~humble(john)<~>brave(john)))<=>(?[X]:((~calm(X)<~>~patient(X)))))&
((?[X]:((quiet(X)&~patient(X))))=>((~curious(mary)&~rich(mary))))&
((tall(fred)&~quiet(fred)))&
((~quiet(susan)&~generous(susan)))&
(?[X]:(~old(X)))&
((rich(alice)|~curious(alice)))&
(calm(susan))&
((~generous(alice)&calm(alice))) | ~generous(paul) | [
"p0",
"p1",
"p2",
"p5",
"p8",
"p10",
"p11",
"p12",
"p13",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 4891451290145317550880923
% SZS output start Proof for 4891451290145317550880923
1. ! [X0] : ((~happy(X0) <~> brave(X0)) <=> calm(X0)) [input p0]
2. ! [X0] : (rich(X0) <=> (strong(X0) & quiet(X0))) [input p1]
3. ? [X0] : (old(X0) | ~patient(X0)) <=> (patient(lucy) & ~quiet(lucy)) [input p2]
6. (rich(fred) & ~creative(fred)) <=> ? [X0] : (~kind(X0) | ~humble(X0)) [input p5]
9. ! [X0] : ((~curious(X0) | ~strong(X0)) <=> (~funny(X0) & calm(X0))) [input p8]
11. ! [X0] : ((generous(X0) <~> happy(X0)) <=> ~generous(X0)) [input p10]
12. (~quiet(lucy) | ~brave(lucy)) <=> (~generous(paul) & humble(paul)) [input p11]
13. funny(lucy) <=> ? [X0] : (~happy(X0) | kind(X0)) [input p12]
14. ! [X0] : ((rich(X0) <~> ~calm(X0)) => old(X0)) [input p13]
17. ~quiet(fred) & tall(fred) [input p16]
23. generous(paul) [input hypothesis]
29. ! [X0] : (old(X0) | (rich(X0) <=> ~calm(X0))) [ennf transformation 14]
31. ! [X0] : ((((~brave(X0) | happy(X0)) & (brave(X0) | ~happy(X0))) | ~calm(X0)) & (calm(X0) | ((~happy(X0) | ~brave(X0)) & (brave(X0) | happy(X0))))) [nnf transformation 1]
32. ! [X0] : ((rich(X0) | (~strong(X0) | ~quiet(X0))) & ((strong(X0) & quiet(X0)) | ~rich(X0))) [nnf transformation 2]
33. ! [X0] : ((rich(X0) | ~strong(X0) | ~quiet(X0)) & ((strong(X0) & quiet(X0)) | ~rich(X0))) [flattening 32]
34. (? [X0] : (old(X0) | ~patient(X0)) | (~patient(lucy) | quiet(lucy))) & ((patient(lucy) & ~quiet(lucy)) | ! [X0] : (~old(X0) & patient(X0))) [nnf transformation 3]
35. (? [X0] : (old(X0) | ~patient(X0)) | ~patient(lucy) | quiet(lucy)) & ((patient(lucy) & ~quiet(lucy)) | ! [X0] : (~old(X0) & patient(X0))) [flattening 34]
36. (? [X0] : (old(X0) | ~patient(X0)) | ~patient(lucy) | quiet(lucy)) & ((patient(lucy) & ~quiet(lucy)) | ! [X1] : (~old(X1) & patient(X1))) [rectify 35]
37. ? [X0] : (old(X0) | ~patient(X0)) => (old(sK0) | ~patient(sK0)) [choice axiom]
38. ((old(sK0) | ~patient(sK0)) | ~patient(lucy) | quiet(lucy)) & ((patient(lucy) & ~quiet(lucy)) | ! [X1] : (~old(X1) & patient(X1))) [skolemisation 36,37]
41. ((rich(fred) & ~creative(fred)) | ! [X0] : (kind(X0) & humble(X0))) & (? [X0] : (~kind(X0) | ~humble(X0)) | (~rich(fred) | creative(fred))) [nnf transformation 6]
42. ((rich(fred) & ~creative(fred)) | ! [X0] : (kind(X0) & humble(X0))) & (? [X0] : (~kind(X0) | ~humble(X0)) | ~rich(fred) | creative(fred)) [flattening 41]
43. ((rich(fred) & ~creative(fred)) | ! [X0] : (kind(X0) & humble(X0))) & (? [X1] : (~kind(X1) | ~humble(X1)) | ~rich(fred) | creative(fred)) [rectify 42]
44. ? [X1] : (~kind(X1) | ~humble(X1)) => (~kind(sK1) | ~humble(sK1)) [choice axiom]
45. ((rich(fred) & ~creative(fred)) | ! [X0] : (kind(X0) & humble(X0))) & ((~kind(sK1) | ~humble(sK1)) | ~rich(fred) | creative(fred)) [skolemisation 43,44]
51. ! [X0] : (((~curious(X0) | ~strong(X0)) | (funny(X0) | ~calm(X0))) & ((~funny(X0) & calm(X0)) | (curious(X0) & strong(X0)))) [nnf transformation 9]
52. ! [X0] : ((~curious(X0) | ~strong(X0) | funny(X0) | ~calm(X0)) & ((~funny(X0) & calm(X0)) | (curious(X0) & strong(X0)))) [flattening 51]
54. ! [X0] : ((((~happy(X0) | ~generous(X0)) & (happy(X0) | generous(X0))) | generous(X0)) & (~generous(X0) | ((generous(X0) | ~happy(X0)) & (happy(X0) | ~generous(X0))))) [nnf transformation 11]
55. ((~quiet(lucy) | ~brave(lucy)) | (generous(paul) | ~humble(paul))) & ((~generous(paul) & humble(paul)) | (quiet(lucy) & brave(lucy))) [nnf transformation 12]
56. (~quiet(lucy) | ~brave(lucy) | generous(paul) | ~humble(paul)) & ((~generous(paul) & humble(paul)) | (quiet(lucy) & brave(lucy))) [flattening 55]
57. (funny(lucy) | ! [X0] : (happy(X0) & ~kind(X0))) & (? [X0] : (~happy(X0) | kind(X0)) | ~funny(lucy)) [nnf transformation 13]
58. (funny(lucy) | ! [X0] : (happy(X0) & ~kind(X0))) & (? [X1] : (~happy(X1) | kind(X1)) | ~funny(lucy)) [rectify 57]
59. ? [X1] : (~happy(X1) | kind(X1)) => (~happy(sK3) | kind(sK3)) [choice axiom]
60. (funny(lucy) | ! [X0] : (happy(X0) & ~kind(X0))) & ((~happy(sK3) | kind(sK3)) | ~funny(lucy)) [skolemisation 58,59]
61. ! [X0] : (old(X0) | ((rich(X0) | calm(X0)) & (~calm(X0) | ~rich(X0)))) [nnf transformation 29]
69. ~brave(X0) | ~happy(X0) | calm(X0) [cnf transformation 31]
72. ~rich(X0) | quiet(X0) [cnf transformation 33]
74. ~strong(X0) | rich(X0) | ~quiet(X0) [cnf transformation 33]
76. ~quiet(lucy) | ~old(X1) [cnf transformation 38]
90. rich(fred) | kind(X0) [cnf transformation 45]
105. ~funny(X0) | strong(X0) [cnf transformation 52]
112. ~generous(X0) | happy(X0) | ~generous(X0) [cnf transformation 54]
114. happy(X0) | generous(X0) | generous(X0) [cnf transformation 54]
118. ~generous(paul) | brave(lucy) [cnf transformation 56]
119. ~generous(paul) | quiet(lucy) [cnf transformation 56]
122. funny(lucy) | ~kind(X0) [cnf transformation 60]
124. ~rich(X0) | ~calm(X0) | old(X0) [cnf transformation 61]
137. ~quiet(fred) [cnf transformation 17]
145. generous(paul) [cnf transformation 23]
146. ~generous(X0) | happy(X0) [duplicate literal removal 112]
147. generous(X0) | happy(X0) [duplicate literal removal 114]
149. 1 <=> quiet(lucy) [avatar definition]
151. quiet(lucy) <- (1) [avatar component clause 149]
166. 5 <=> ! [X1] : ~old(X1) [avatar definition]
167. ~old(X1) <- (5) [avatar component clause 166]
173. 5 | ~1 [avatar split clause 76,149,166]
176. 7 <=> ! [X0] : kind(X0) [avatar definition]
177. kind(X0) <- (7) [avatar component clause 176]
179. 8 <=> rich(fred) [avatar definition]
181. rich(fred) <- (8) [avatar component clause 179]
182. 7 | 8 [avatar split clause 90,179,176]
224. 18 <=> kind(susan) [avatar definition]
225. ~kind(susan) <- (~18) [avatar component clause 224]
226. kind(susan) <- (18) [avatar component clause 224]
238. happy(X0) [subsumption resolution 146,147]
244. 22 <=> generous(paul) [avatar definition]
248. 23 <=> brave(lucy) [avatar definition]
249. brave(lucy) <- (23) [avatar component clause 248]
252. 1 | ~22 [avatar split clause 119,244,149]
253. 23 | ~22 [avatar split clause 118,244,248]
257. 24 <=> ! [X0] : ~kind(X0) [avatar definition]
258. ~kind(X0) <- (24) [avatar component clause 257]
260. 25 <=> funny(lucy) [avatar definition]
262. funny(lucy) <- (25) [avatar component clause 260]
263. 24 | 25 [avatar split clause 122,260,257]
322. 22 [avatar split clause 145,244]
325. $false <- (18, 24) [subsumption resolution 226,258]
326. ~18 | ~24 [avatar contradiction clause 325]
338. quiet(fred) <- (8) [resolution 72,181]
340. $false <- (8) [subsumption resolution 338,137]
341. ~8 [avatar contradiction clause 340]
342. $false <- (7, ~18) [resolution 177,225]
343. ~7 | 18 [avatar contradiction clause 342]
347. strong(lucy) <- (25) [resolution 105,262]
360. ~happy(lucy) | calm(lucy) <- (23) [resolution 69,249]
378. rich(lucy) | ~quiet(lucy) <- (25) [resolution 74,347]
379. rich(lucy) <- (1, 25) [subsumption resolution 378,151]
383. calm(lucy) <- (23) [subsumption resolution 360,238]
413. ~calm(lucy) | old(lucy) <- (1, 25) [resolution 124,379]
417. old(lucy) <- (1, 23, 25) [subsumption resolution 413,383]
418. $false <- (1, 5, 23, 25) [subsumption resolution 417,167]
419. ~1 | ~5 | ~23 | ~25 [avatar contradiction clause 418]
420. $false [avatar sat refutation 173,182,252,253,263,322,326,341,343,419]
% SZS output end Proof for 4891451290145317550880923
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is patient or quiet is creative or not humble.
Everyone who is both brave and creative is not brave or not generous and vice versa.
Everyone who is both creative and not patient is either brave or rich.
If someone is either creative or not creative then someone is not old.
If someone is patient or funny then lucy is calm or not brave.
Everyone who is not creative is either not tall or patient and vice versa.
Everyone who is either brave or curious is strong.
Everyone who is not old is rich or old and vice versa.
If someone is strong or not kind then alice is quiet or humble.
If fred is not quiet or humble then susan is quiet or not brave and vice versa.
If lucy is both not calm and not funny then fred is either patient or not generous.
If paul is both not calm and not generous then someone is not patient or wise.
If someone is either brave or not rich then someone is both brave and not quiet and vice versa.
Everyone who is both not strong and wise is not funny.
If john is calm then someone is not wise or not humble.
If lucy is both rich and not patient then someone is not quiet or calm and vice versa.
Someone is not quiet.
Someone is either not funny or rich.
Fred is not kind.
Someone is either quiet or creative.
Someone is curious or funny.
Susan is generous.
Someone is either not funny or not tall. | Fred is not quiet. | neutral | (![X]:((patient(X)|quiet(X))=>(creative(X)|~humble(X))))&
(![X]:((brave(X)&creative(X))<=>(~brave(X)|~generous(X))))&
(![X]:((creative(X)&~patient(X))=>(brave(X)<~>rich(X))))&
((?[X]:((creative(X)<~>~creative(X))))=>(?[X]:(~old(X))))&
((?[X]:((patient(X)|funny(X))))=>((calm(lucy)|~brave(lucy))))&
(![X]:(~creative(X)<=>(~tall(X)<~>patient(X))))&
(![X]:((brave(X)<~>curious(X))=>strong(X)))&
(![X]:(~old(X)<=>(rich(X)|old(X))))&
((?[X]:((strong(X)|~kind(X))))=>((quiet(alice)|humble(alice))))&
(((~quiet(fred)|humble(fred)))<=>((quiet(susan)|~brave(susan))))&
(((~calm(lucy)&~funny(lucy)))=>((patient(fred)<~>~generous(fred))))&
(((~calm(paul)&~generous(paul)))=>(?[X]:((~patient(X)|wise(X)))))&
((?[X]:((brave(X)<~>~rich(X))))<=>(?[X]:((brave(X)&~quiet(X)))))&
(![X]:((~strong(X)&wise(X))=>~funny(X)))&
((calm(john))=>(?[X]:((~wise(X)|~humble(X)))))&
(((rich(lucy)&~patient(lucy)))<=>(?[X]:((~quiet(X)|calm(X)))))&
(?[X]:(~quiet(X)))&
(?[X]:((~funny(X)<~>rich(X))))&
(~kind(fred))&
(?[X]:((quiet(X)<~>creative(X))))&
(?[X]:((curious(X)|funny(X))))&
(generous(susan))&
(?[X]:((~funny(X)<~>~tall(X)))) | ~quiet(fred) | [] | null | 0 |
Everyone who is happy is both not generous and not quiet and vice versa.
Everyone who is kind or rich is both not generous and not brave.
Everyone who is both rich and not brave is not tall or not strong.
If paul is not patient then someone is not kind or patient.
Everyone who is either not creative or curious is not kind or not humble.
Everyone who is either quiet or not brave is not strong or wise and vice versa.
Everyone who is either rich or old is not rich.
If mary is either curious or not wise then someone is either not wise or tall and vice versa.
If lucy is not curious then susan is calm or not funny.
If someone is either not quiet or not old then someone is both wise and not wise and vice versa.
Everyone who is not strong is not patient.
If lucy is both not creative and not patient then alice is either tall or not calm and vice versa.
Everyone who is not old or kind is either not brave or funny and vice versa.
Everyone who is both patient and rich is either not brave or brave and vice versa.
If lucy is both creative and old then fred is either brave or not rich.
Fred is not wise.
Someone is either not brave or not strong.
Someone is not brave.
Someone is not curious.
Someone is either old or tall.
Susan is both calm and not funny. | Paul is brave. | contradiction | (![X]:(happy(X)<=>(~generous(X)&~quiet(X))))&
(![X]:((kind(X)|rich(X))=>(~generous(X)&~brave(X))))&
(![X]:((rich(X)&~brave(X))=>(~tall(X)|~strong(X))))&
((~patient(paul))=>(?[X]:((~kind(X)|patient(X)))))&
(![X]:((~creative(X)<~>curious(X))=>(~kind(X)|~humble(X))))&
(![X]:((quiet(X)<~>~brave(X))<=>(~strong(X)|wise(X))))&
(![X]:((rich(X)<~>old(X))=>~rich(X)))&
(((curious(mary)<~>~wise(mary)))<=>(?[X]:((~wise(X)<~>tall(X)))))&
((~curious(lucy))=>((calm(susan)|~funny(susan))))&
((?[X]:((~quiet(X)<~>~old(X))))<=>(?[X]:((wise(X)&~wise(X)))))&
(![X]:(~strong(X)=>~patient(X)))&
(((~creative(lucy)&~patient(lucy)))<=>((tall(alice)<~>~calm(alice))))&
(![X]:((~old(X)|kind(X))<=>(~brave(X)<~>funny(X))))&
(![X]:((patient(X)&rich(X))<=>(~brave(X)<~>brave(X))))&
(((creative(lucy)&old(lucy)))=>((brave(fred)<~>~rich(fred))))&
(~wise(fred))&
(?[X]:((~brave(X)<~>~strong(X))))&
(?[X]:(~brave(X)))&
(?[X]:(~curious(X)))&
(?[X]:((old(X)<~>tall(X))))&
((calm(susan)&~funny(susan))) | brave(paul) | [
"p1",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 884241075968549335572050
% SZS output start Proof for 884241075968549335572050
2. ! [X0] : ((rich(X0) | kind(X0)) => (~brave(X0) & ~generous(X0))) [input p1]
14. ! [X0] : ((rich(X0) & patient(X0)) <=> (~brave(X0) <~> brave(X0))) [input p13]
22. brave(paul) [input hypothesis]
24. ! [X0] : ((rich(X0) | kind(X0)) => ~brave(X0)) [pure predicate removal 2]
26. ! [X0] : (~brave(X0) | (~rich(X0) & ~kind(X0))) [ennf transformation 24]
54. ! [X0] : (((rich(X0) & patient(X0)) | ((~brave(X0) | ~brave(X0)) & (brave(X0) | brave(X0)))) & (((~brave(X0) | brave(X0)) & (brave(X0) | ~brave(X0))) | (~rich(X0) | ~patient(X0)))) [nnf transformation 14]
55. ! [X0] : (((rich(X0) & patient(X0)) | ((~brave(X0) | ~brave(X0)) & (brave(X0) | brave(X0)))) & (((~brave(X0) | brave(X0)) & (brave(X0) | ~brave(X0))) | ~rich(X0) | ~patient(X0))) [flattening 54]
68. ~brave(X0) | ~rich(X0) [cnf transformation 26]
112. rich(X0) | ~brave(X0) | ~brave(X0) [cnf transformation 55]
124. brave(paul) [cnf transformation 22]
128. rich(X0) | ~brave(X0) [duplicate literal removal 112]
225. ~brave(X0) [subsumption resolution 128,68]
248. $false [subsumption resolution 124,225]
% SZS output end Proof for 884241075968549335572050
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If lucy is not strong or brave then paul is quiet or not quiet.
If mary is both calm and kind then alice is not old or not wise and vice versa.
Everyone who is both curious and quiet is either not generous or not brave.
Everyone who is both old and not happy is not wise or not patient and vice versa.
Everyone who is both wise and calm is generous or quiet.
Everyone who is either not curious or not wise is not rich.
Everyone who is not generous is happy or not kind and vice versa.
Everyone who is both wise and tall is both brave and rich and vice versa.
Everyone who is either humble or wise is either not strong or not curious.
Everyone who is not humble or not rich is kind.
Everyone who is either generous or not brave is both wise and creative and vice versa.
Everyone who is both not old and not quiet is either kind or not rich and vice versa.
Everyone who is brave or not humble is not brave.
If mary is not brave or humble then someone is happy and vice versa.
If someone is rich then susan is quiet and vice versa.
Everyone who is not funny or patient is either not brave or kind and vice versa.
Someone is generous or calm.
Alice is curious or not rich.
Susan is not wise or not strong.
Fred is not kind or quiet.
Lucy is tall.
Mary is either not funny or not humble. | Fred is not kind. | neutral | (((~strong(lucy)|brave(lucy)))=>((quiet(paul)|~quiet(paul))))&
(((calm(mary)&kind(mary)))<=>((~old(alice)|~wise(alice))))&
(![X]:((curious(X)&quiet(X))=>(~generous(X)<~>~brave(X))))&
(![X]:((old(X)&~happy(X))<=>(~wise(X)|~patient(X))))&
(![X]:((wise(X)&calm(X))=>(generous(X)|quiet(X))))&
(![X]:((~curious(X)<~>~wise(X))=>~rich(X)))&
(![X]:(~generous(X)<=>(happy(X)|~kind(X))))&
(![X]:((wise(X)&tall(X))<=>(brave(X)&rich(X))))&
(![X]:((humble(X)<~>wise(X))=>(~strong(X)<~>~curious(X))))&
(![X]:((~humble(X)|~rich(X))=>kind(X)))&
(![X]:((generous(X)<~>~brave(X))<=>(wise(X)&creative(X))))&
(![X]:((~old(X)&~quiet(X))<=>(kind(X)<~>~rich(X))))&
(![X]:((brave(X)|~humble(X))=>~brave(X)))&
(((~brave(mary)|humble(mary)))<=>(?[X]:(happy(X))))&
((?[X]:(rich(X)))<=>(quiet(susan)))&
(![X]:((~funny(X)|patient(X))<=>(~brave(X)<~>kind(X))))&
(?[X]:((generous(X)|calm(X))))&
((curious(alice)|~rich(alice)))&
((~wise(susan)|~strong(susan)))&
((~kind(fred)|quiet(fred)))&
(tall(lucy))&
((~funny(mary)<~>~humble(mary))) | ~kind(fred) | [] | null | 0 |
Everyone who is both happy and not patient is either not curious or generous.
Everyone who is either not creative or patient is calm or not rich.
Everyone who is both generous and not creative is either not tall or brave.
If someone is both happy and patient then someone is not humble and vice versa.
If someone is not patient then someone is not creative or not old and vice versa.
If paul is either not tall or tall then fred is both strong and calm and vice versa.
If someone is either curious or brave then someone is either funny or not funny.
Everyone who is not curious is quiet and vice versa.
Everyone who is not quiet is not curious or happy and vice versa.
If john is not funny or quiet then someone is either not kind or curious.
Everyone who is either not patient or happy is either brave or not brave and vice versa.
Everyone who is both not happy and rich is both not quiet and brave and vice versa.
Everyone who is not strong or not brave is strong or not generous.
Everyone who is not funny is both not brave and not tall and vice versa.
If susan is not wise then paul is either humble or not curious and vice versa.
Everyone who is both not creative and patient is either tall or not kind and vice versa.
Susan is generous or strong.
Fred is both not rich and patient.
John is either patient or rich.
Someone is either not funny or tall. | Susan is quiet. | contradiction | (![X]:((happy(X)&~patient(X))=>(~curious(X)<~>generous(X))))&
(![X]:((~creative(X)<~>patient(X))=>(calm(X)|~rich(X))))&
(![X]:((generous(X)&~creative(X))=>(~tall(X)<~>brave(X))))&
((?[X]:((happy(X)&patient(X))))<=>(?[X]:(~humble(X))))&
((?[X]:(~patient(X)))<=>(?[X]:((~creative(X)|~old(X)))))&
(((~tall(paul)<~>tall(paul)))<=>((strong(fred)&calm(fred))))&
((?[X]:((curious(X)<~>brave(X))))=>(?[X]:((funny(X)<~>~funny(X)))))&
(![X]:(~curious(X)<=>quiet(X)))&
(![X]:(~quiet(X)<=>(~curious(X)|happy(X))))&
(((~funny(john)|quiet(john)))=>(?[X]:((~kind(X)<~>curious(X)))))&
(![X]:((~patient(X)<~>happy(X))<=>(brave(X)<~>~brave(X))))&
(![X]:((~happy(X)&rich(X))<=>(~quiet(X)&brave(X))))&
(![X]:((~strong(X)|~brave(X))=>(strong(X)|~generous(X))))&
(![X]:(~funny(X)<=>(~brave(X)&~tall(X))))&
((~wise(susan))<=>((humble(paul)<~>~curious(paul))))&
(![X]:((~creative(X)&patient(X))<=>(tall(X)<~>~kind(X))))&
((generous(susan)|strong(susan)))&
((~rich(fred)&patient(fred)))&
((patient(john)<~>rich(john)))&
(?[X]:((~funny(X)<~>tall(X)))) | quiet(susan) | [
"p7",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 4213941611990670482619850
% SZS output start Proof for 4213941611990670482619850
8. ! [X0] : (~curious(X0) <=> quiet(X0)) [input p7]
9. ! [X0] : (~quiet(X0) <=> (happy(X0) | ~curious(X0))) [input p8]
21. quiet(susan) [input hypothesis]
54. ! [X0] : ((~curious(X0) | ~quiet(X0)) & (quiet(X0) | curious(X0))) [nnf transformation 8]
55. ! [X0] : ((~quiet(X0) | (~happy(X0) & curious(X0))) & ((happy(X0) | ~curious(X0)) | quiet(X0))) [nnf transformation 9]
56. ! [X0] : ((~quiet(X0) | (~happy(X0) & curious(X0))) & (happy(X0) | ~curious(X0) | quiet(X0))) [flattening 55]
95. ~curious(X0) | ~quiet(X0) [cnf transformation 54]
97. ~quiet(X0) | curious(X0) [cnf transformation 56]
137. quiet(susan) [cnf transformation 21]
208. ~quiet(X0) [subsumption resolution 97,95]
264. $false [subsumption resolution 137,208]
% SZS output end Proof for 4213941611990670482619850
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not tall and wise is quiet or not kind and vice versa.
Everyone who is calm or not rich is patient or not rich and vice versa.
If someone is either not creative or brave then alice is either not quiet or calm and vice versa.
If lucy is either not curious or not patient then someone is both wise and not funny and vice versa.
Everyone who is either not old or tall is both generous and old.
Everyone who is curious or generous is not creative or not tall and vice versa.
Everyone who is both not tall and humble is strong and vice versa.
If fred is both funny and not kind then someone is not humble or calm and vice versa.
If susan is either rich or wise then someone is calm or wise and vice versa.
Everyone who is patient is either generous or not tall and vice versa.
Everyone who is not tall or not rich is calm.
If mary is both humble and not patient then susan is not kind and vice versa.
If someone is either not funny or strong then mary is either tall or not calm and vice versa.
Everyone who is either wise or not calm is not tall or wise.
If john is happy then someone is wise and vice versa.
Someone is not wise or happy.
Someone is either not generous or creative.
Someone is either rich or not creative.
Lucy is either not humble or humble.
Someone is either creative or not wise.
Fred is either rich or humble. | Mary is kind. | neutral | (![X]:((~tall(X)&wise(X))<=>(quiet(X)|~kind(X))))&
(![X]:((calm(X)|~rich(X))<=>(patient(X)|~rich(X))))&
((?[X]:((~creative(X)<~>brave(X))))<=>((~quiet(alice)<~>calm(alice))))&
(((~curious(lucy)<~>~patient(lucy)))<=>(?[X]:((wise(X)&~funny(X)))))&
(![X]:((~old(X)<~>tall(X))=>(generous(X)&old(X))))&
(![X]:((curious(X)|generous(X))<=>(~creative(X)|~tall(X))))&
(![X]:((~tall(X)&humble(X))<=>strong(X)))&
(((funny(fred)&~kind(fred)))<=>(?[X]:((~humble(X)|calm(X)))))&
(((rich(susan)<~>wise(susan)))<=>(?[X]:((calm(X)|wise(X)))))&
(![X]:(patient(X)<=>(generous(X)<~>~tall(X))))&
(![X]:((~tall(X)|~rich(X))=>calm(X)))&
(((humble(mary)&~patient(mary)))<=>(~kind(susan)))&
((?[X]:((~funny(X)<~>strong(X))))<=>((tall(mary)<~>~calm(mary))))&
(![X]:((wise(X)<~>~calm(X))=>(~tall(X)|wise(X))))&
((happy(john))<=>(?[X]:(wise(X))))&
(?[X]:((~wise(X)|happy(X))))&
(?[X]:((~generous(X)<~>creative(X))))&
(?[X]:((rich(X)<~>~creative(X))))&
((~humble(lucy)<~>humble(lucy)))&
(?[X]:((creative(X)<~>~wise(X))))&
((rich(fred)<~>humble(fred))) | kind(mary) | [] | null | 0 |
If someone is humble or funny then someone is not tall.
Everyone who is both happy and not generous is either not wise or not happy and vice versa.
If susan is not tall or not funny then lucy is either creative or not creative and vice versa.
Everyone who is either old or quiet is not patient or curious and vice versa.
Everyone who is both not quiet and not rich is both patient and not tall.
Everyone who is not wise or calm is both not generous and calm and vice versa.
Everyone who is either quiet or not calm is brave or curious.
Everyone who is both humble and not wise is not calm or patient and vice versa.
If fred is wise or happy then someone is old or brave and vice versa.
If lucy is both quiet and not brave then paul is not tall or curious.
Everyone who is both rich and patient is not calm.
Everyone who is calm is both tall and quiet.
Everyone who is not strong or creative is not humble and vice versa.
Everyone who is strong or generous is either not humble or wise.
Paul is strong or not brave.
Fred is either not funny or not strong.
Someone is either not curious or not humble.
Someone is not creative.
Lucy is either calm or old.
Someone is either old or not happy. | Lucy is not strong. | neutral | ((?[X]:((humble(X)|funny(X))))=>(?[X]:(~tall(X))))&
(![X]:((happy(X)&~generous(X))<=>(~wise(X)<~>~happy(X))))&
(((~tall(susan)|~funny(susan)))<=>((creative(lucy)<~>~creative(lucy))))&
(![X]:((old(X)<~>quiet(X))<=>(~patient(X)|curious(X))))&
(![X]:((~quiet(X)&~rich(X))=>(patient(X)&~tall(X))))&
(![X]:((~wise(X)|calm(X))<=>(~generous(X)&calm(X))))&
(![X]:((quiet(X)<~>~calm(X))=>(brave(X)|curious(X))))&
(![X]:((humble(X)&~wise(X))<=>(~calm(X)|patient(X))))&
(((wise(fred)|happy(fred)))<=>(?[X]:((old(X)|brave(X)))))&
(((quiet(lucy)&~brave(lucy)))=>((~tall(paul)|curious(paul))))&
(![X]:((rich(X)&patient(X))=>~calm(X)))&
(![X]:(calm(X)=>(tall(X)&quiet(X))))&
(![X]:((~strong(X)|creative(X))<=>~humble(X)))&
(![X]:((strong(X)|generous(X))=>(~humble(X)<~>wise(X))))&
((strong(paul)|~brave(paul)))&
((~funny(fred)<~>~strong(fred)))&
(?[X]:((~curious(X)<~>~humble(X))))&
(?[X]:(~creative(X)))&
((calm(lucy)<~>old(lucy)))&
(?[X]:((old(X)<~>~happy(X)))) | ~strong(lucy) | [] | null | 0 |
Everyone who is either not generous or brave is not quiet and vice versa.
Everyone who is either funny or not tall is funny or not tall and vice versa.
Everyone who is both tall and not curious is calm.
Everyone who is not generous or not brave is humble and vice versa.
Everyone who is both not generous and brave is rich and vice versa.
Everyone who is old is generous.
Everyone who is both creative and happy is happy or curious and vice versa.
Everyone who is either not calm or not wise is wise.
Everyone who is both strong and humble is either not creative or not quiet and vice versa.
If fred is both not quiet and tall then someone is curious.
Everyone who is kind is not calm and vice versa.
If susan is either patient or not wise then mary is not wise or curious.
If mary is not funny or not calm then susan is not curious.
If someone is not strong then fred is both generous and kind and vice versa.
Everyone who is both not quiet and creative is funny or happy.
If someone is not old or not rich then someone is either not quiet or kind.
Someone is both rich and tall.
Someone is not kind or wise.
Alice is either old or tall.
Someone is curious or kind.
Alice is both not calm and tall.
Alice is either kind or rich.
Someone is calm or not calm.
Someone is calm or not kind. | Alice is humble. | entailment | (![X]:((~generous(X)<~>brave(X))<=>~quiet(X)))&
(![X]:((funny(X)<~>~tall(X))<=>(funny(X)|~tall(X))))&
(![X]:((tall(X)&~curious(X))=>calm(X)))&
(![X]:((~generous(X)|~brave(X))<=>humble(X)))&
(![X]:((~generous(X)&brave(X))<=>rich(X)))&
(![X]:(old(X)=>generous(X)))&
(![X]:((creative(X)&happy(X))<=>(happy(X)|curious(X))))&
(![X]:((~calm(X)<~>~wise(X))=>wise(X)))&
(![X]:((strong(X)&humble(X))<=>(~creative(X)<~>~quiet(X))))&
(((~quiet(fred)&tall(fred)))=>(?[X]:(curious(X))))&
(![X]:(kind(X)<=>~calm(X)))&
(((patient(susan)<~>~wise(susan)))=>((~wise(mary)|curious(mary))))&
(((~funny(mary)|~calm(mary)))=>(~curious(susan)))&
((?[X]:(~strong(X)))<=>((generous(fred)&kind(fred))))&
(![X]:((~quiet(X)&creative(X))=>(funny(X)|happy(X))))&
((?[X]:((~old(X)|~rich(X))))=>(?[X]:((~quiet(X)<~>kind(X)))))&
(?[X]:((rich(X)&tall(X))))&
(?[X]:((~kind(X)|wise(X))))&
((old(alice)<~>tall(alice)))&
(?[X]:((curious(X)|kind(X))))&
((~calm(alice)&tall(alice)))&
((kind(alice)<~>rich(alice)))&
(?[X]:((calm(X)|~calm(X))))&
(?[X]:((calm(X)|~kind(X)))) | humble(alice) | [
"p0",
"p2",
"p3",
"p6",
"p8",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 7785342522099733079561236
% SZS output start Proof for 7785342522099733079561236
1. ! [X0] : ((~generous(X0) <~> brave(X0)) <=> ~quiet(X0)) [input p0]
3. ! [X0] : ((~curious(X0) & tall(X0)) => calm(X0)) [input p2]
4. ! [X0] : ((~brave(X0) | ~generous(X0)) <=> humble(X0)) [input p3]
7. ! [X0] : ((happy(X0) & creative(X0)) <=> (curious(X0) | happy(X0))) [input p6]
9. ! [X0] : ((humble(X0) & strong(X0)) <=> (~creative(X0) <~> ~quiet(X0))) [input p8]
21. tall(alice) & ~calm(alice) [input p20]
25. ~humble(alice) [input hypothesis]
27. ! [X0] : (calm(X0) | (curious(X0) | ~tall(X0))) [ennf transformation 3]
28. ! [X0] : (calm(X0) | curious(X0) | ~tall(X0)) [flattening 27]
39. ! [X0] : ((((~brave(X0) | generous(X0)) & (brave(X0) | ~generous(X0))) | quiet(X0)) & (~quiet(X0) | ((~generous(X0) | ~brave(X0)) & (brave(X0) | generous(X0))))) [nnf transformation 1]
42. ! [X0] : (((~brave(X0) | ~generous(X0)) | ~humble(X0)) & (humble(X0) | (brave(X0) & generous(X0)))) [nnf transformation 4]
43. ! [X0] : ((~brave(X0) | ~generous(X0) | ~humble(X0)) & (humble(X0) | (brave(X0) & generous(X0)))) [flattening 42]
46. ! [X0] : (((happy(X0) & creative(X0)) | (~curious(X0) & ~happy(X0))) & ((curious(X0) | happy(X0)) | (~happy(X0) | ~creative(X0)))) [nnf transformation 7]
47. ! [X0] : (((happy(X0) & creative(X0)) | (~curious(X0) & ~happy(X0))) & (curious(X0) | happy(X0) | ~happy(X0) | ~creative(X0))) [flattening 46]
49. ! [X0] : (((humble(X0) & strong(X0)) | ((~creative(X0) | quiet(X0)) & (~quiet(X0) | creative(X0)))) & (((quiet(X0) | creative(X0)) & (~quiet(X0) | ~creative(X0))) | (~humble(X0) | ~strong(X0)))) [nnf transformation 9]
50. ! [X0] : (((humble(X0) & strong(X0)) | ((~creative(X0) | quiet(X0)) & (~quiet(X0) | creative(X0)))) & (((quiet(X0) | creative(X0)) & (~quiet(X0) | ~creative(X0))) | ~humble(X0) | ~strong(X0))) [flattening 49]
77. ~quiet(X0) | ~generous(X0) | ~brave(X0) [cnf transformation 39]
86. ~tall(X0) | curious(X0) | calm(X0) [cnf transformation 28]
87. humble(X0) | generous(X0) [cnf transformation 43]
88. humble(X0) | brave(X0) [cnf transformation 43]
96. ~curious(X0) | creative(X0) [cnf transformation 47]
106. ~creative(X0) | humble(X0) | quiet(X0) [cnf transformation 50]
128. ~calm(alice) [cnf transformation 21]
129. tall(alice) [cnf transformation 21]
134. ~humble(alice) [cnf transformation 25]
235. 22 <=> tall(alice) [avatar definition]
236. tall(alice) <- (22) [avatar component clause 235]
249. 22 [avatar split clause 129,235]
261. generous(alice) [resolution 87,134]
262. brave(alice) [resolution 88,134]
295. curious(alice) | calm(alice) <- (22) [resolution 86,236]
305. curious(alice) <- (22) [subsumption resolution 295,128]
310. creative(alice) <- (22) [resolution 305,96]
348. humble(alice) | quiet(alice) <- (22) [resolution 310,106]
350. quiet(alice) <- (22) [subsumption resolution 348,134]
357. ~generous(alice) | ~brave(alice) <- (22) [resolution 350,77]
359. ~brave(alice) <- (22) [subsumption resolution 357,261]
360. $false <- (22) [subsumption resolution 359,262]
361. ~22 [avatar contradiction clause 360]
362. $false [avatar sat refutation 249,361]
% SZS output end Proof for 7785342522099733079561236
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.040 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both quiet and not curious is either brave or not kind.
Everyone who is either patient or not creative is both not wise and tall.
If someone is both not wise and not rich then lucy is calm or not wise and vice versa.
Everyone who is kind or patient is both not creative and quiet.
Everyone who is either not brave or happy is old or not humble and vice versa.
If someone is calm or creative then someone is either wise or not patient and vice versa.
Everyone who is creative is not happy or not curious and vice versa.
If susan is wise or tall then mary is not calm or not humble.
Everyone who is not strong is patient and vice versa.
Everyone who is rich or quiet is funny or patient.
Everyone who is both humble and creative is funny and vice versa.
Everyone who is both curious and wise is both wise and not strong and vice versa.
Everyone who is both calm and tall is rich and vice versa.
Everyone who is not rich is generous and vice versa.
If john is either not calm or not strong then someone is not rich.
If susan is both not old and curious then someone is humble and vice versa.
Someone is either not brave or calm.
Lucy is not rich or not humble.
Mary is not humble.
Someone is generous or not old.
Someone is either brave or wise.
John is tall.
Someone is either not curious or happy. | Susan is not old. | neutral | (![X]:((quiet(X)&~curious(X))=>(brave(X)<~>~kind(X))))&
(![X]:((patient(X)<~>~creative(X))=>(~wise(X)&tall(X))))&
((?[X]:((~wise(X)&~rich(X))))<=>((calm(lucy)|~wise(lucy))))&
(![X]:((kind(X)|patient(X))=>(~creative(X)&quiet(X))))&
(![X]:((~brave(X)<~>happy(X))<=>(old(X)|~humble(X))))&
((?[X]:((calm(X)|creative(X))))<=>(?[X]:((wise(X)<~>~patient(X)))))&
(![X]:(creative(X)<=>(~happy(X)|~curious(X))))&
(((wise(susan)|tall(susan)))=>((~calm(mary)|~humble(mary))))&
(![X]:(~strong(X)<=>patient(X)))&
(![X]:((rich(X)|quiet(X))=>(funny(X)|patient(X))))&
(![X]:((humble(X)&creative(X))<=>funny(X)))&
(![X]:((curious(X)&wise(X))<=>(wise(X)&~strong(X))))&
(![X]:((calm(X)&tall(X))<=>rich(X)))&
(![X]:(~rich(X)<=>generous(X)))&
(((~calm(john)<~>~strong(john)))=>(?[X]:(~rich(X))))&
(((~old(susan)&curious(susan)))<=>(?[X]:(humble(X))))&
(?[X]:((~brave(X)<~>calm(X))))&
((~rich(lucy)|~humble(lucy)))&
(~humble(mary))&
(?[X]:((generous(X)|~old(X))))&
(?[X]:((brave(X)<~>wise(X))))&
(tall(john))&
(?[X]:((~curious(X)<~>happy(X)))) | ~old(susan) | [] | null | 0 |
If susan is not brave then susan is not old.
If someone is not generous then someone is curious.
If mary is not kind or quiet then fred is both kind and not humble.
Everyone who is either not funny or patient is not kind or not brave.
Everyone who is not quiet is not calm or not brave.
If someone is both happy and not happy then susan is either funny or not wise.
Everyone who is not generous or not rich is not kind.
Everyone who is either humble or quiet is both creative and tall and vice versa.
Everyone who is both brave and strong is either not brave or not generous.
Everyone who is both not calm and not funny is funny and vice versa.
Everyone who is not quiet is either kind or not strong.
Everyone who is not curious or patient is both funny and not generous.
Everyone who is not curious or humble is either not calm or tall and vice versa.
If john is either happy or kind then someone is humble or funny and vice versa.
If someone is either wise or not curious then alice is both not happy and strong and vice versa.
Paul is not creative.
Fred is either not rich or not happy.
Lucy is not tall.
Someone is humble or not tall.
Someone is not rich. | Susan is not generous. | neutral | ((~brave(susan))=>(~old(susan)))&
((?[X]:(~generous(X)))=>(?[X]:(curious(X))))&
(((~kind(mary)|quiet(mary)))=>((kind(fred)&~humble(fred))))&
(![X]:((~funny(X)<~>patient(X))=>(~kind(X)|~brave(X))))&
(![X]:(~quiet(X)=>(~calm(X)|~brave(X))))&
((?[X]:((happy(X)&~happy(X))))=>((funny(susan)<~>~wise(susan))))&
(![X]:((~generous(X)|~rich(X))=>~kind(X)))&
(![X]:((humble(X)<~>quiet(X))<=>(creative(X)&tall(X))))&
(![X]:((brave(X)&strong(X))=>(~brave(X)<~>~generous(X))))&
(![X]:((~calm(X)&~funny(X))<=>funny(X)))&
(![X]:(~quiet(X)=>(kind(X)<~>~strong(X))))&
(![X]:((~curious(X)|patient(X))=>(funny(X)&~generous(X))))&
(![X]:((~curious(X)|humble(X))<=>(~calm(X)<~>tall(X))))&
(((happy(john)<~>kind(john)))<=>(?[X]:((humble(X)|funny(X)))))&
((?[X]:((wise(X)<~>~curious(X))))<=>((~happy(alice)&strong(alice))))&
(~creative(paul))&
((~rich(fred)<~>~happy(fred)))&
(~tall(lucy))&
(?[X]:((humble(X)|~tall(X))))&
(?[X]:(~rich(X))) | ~generous(susan) | [] | null | 0 |
Everyone who is both not patient and not creative is patient and vice versa.
Everyone who is either not quiet or not rich is either rich or wise and vice versa.
Everyone who is calm is either kind or not generous.
If paul is either happy or not happy then lucy is both not funny and generous and vice versa.
Everyone who is not happy or funny is not creative or kind.
If alice is not tall then someone is either not curious or not old.
If someone is either kind or funny then susan is either tall or not humble and vice versa.
Everyone who is kind or not happy is brave.
If someone is both not kind and not quiet then someone is both not tall and not generous.
Everyone who is both quiet and not calm is both generous and not creative.
If someone is not brave then someone is both curious and not curious and vice versa.
If someone is either not kind or tall then someone is not rich.
If someone is either calm or strong then mary is rich or curious.
Everyone who is curious is not tall and vice versa.
Everyone who is not happy is not wise or not kind and vice versa.
If someone is calm or kind then someone is rich.
Someone is not rich or not patient.
Someone is strong or not calm.
Someone is both not generous and tall.
Alice is not funny.
Mary is not tall.
Someone is either tall or rich.
Lucy is not creative or not strong.
Someone is both not wise and not strong. | Lucy is creative. | entailment | (![X]:((~patient(X)&~creative(X))<=>patient(X)))&
(![X]:((~quiet(X)<~>~rich(X))<=>(rich(X)<~>wise(X))))&
(![X]:(calm(X)=>(kind(X)<~>~generous(X))))&
(((happy(paul)<~>~happy(paul)))<=>((~funny(lucy)&generous(lucy))))&
(![X]:((~happy(X)|funny(X))=>(~creative(X)|kind(X))))&
((~tall(alice))=>(?[X]:((~curious(X)<~>~old(X)))))&
((?[X]:((kind(X)<~>funny(X))))<=>((tall(susan)<~>~humble(susan))))&
(![X]:((kind(X)|~happy(X))=>brave(X)))&
((?[X]:((~kind(X)&~quiet(X))))=>(?[X]:((~tall(X)&~generous(X)))))&
(![X]:((quiet(X)&~calm(X))=>(generous(X)&~creative(X))))&
((?[X]:(~brave(X)))<=>(?[X]:((curious(X)&~curious(X)))))&
((?[X]:((~kind(X)<~>tall(X))))=>(?[X]:(~rich(X))))&
((?[X]:((calm(X)<~>strong(X))))=>((rich(mary)|curious(mary))))&
(![X]:(curious(X)<=>~tall(X)))&
(![X]:(~happy(X)<=>(~wise(X)|~kind(X))))&
((?[X]:((calm(X)|kind(X))))=>(?[X]:(rich(X))))&
(?[X]:((~rich(X)|~patient(X))))&
(?[X]:((strong(X)|~calm(X))))&
(?[X]:((~generous(X)&tall(X))))&
(~funny(alice))&
(~tall(mary))&
(?[X]:((tall(X)<~>rich(X))))&
((~creative(lucy)|~strong(lucy)))&
(?[X]:((~wise(X)&~strong(X)))) | creative(lucy) | [
"p0",
"hypothesis"
] | % SZS status Unsatisfiable for 803327881190559997718960
% SZS output start Proof for 803327881190559997718960
1. ! [X0] : ((~creative(X0) & ~patient(X0)) <=> patient(X0)) [input p0]
25. ~creative(lucy) [input hypothesis]
42. ! [X0] : (((~creative(X0) & ~patient(X0)) | ~patient(X0)) & (patient(X0) | (creative(X0) | patient(X0)))) [nnf transformation 1]
43. ! [X0] : (((~creative(X0) & ~patient(X0)) | ~patient(X0)) & (patient(X0) | creative(X0) | patient(X0))) [flattening 42]
85. patient(X0) | creative(X0) | patient(X0) [cnf transformation 43]
86. ~patient(X0) | ~patient(X0) [cnf transformation 43]
147. ~creative(lucy) [cnf transformation 25]
156. patient(X0) | creative(X0) [duplicate literal removal 85]
157. ~patient(X0) [duplicate literal removal 86]
158. creative(X0) [subsumption resolution 156,157]
296. $false [subsumption resolution 147,158]
% SZS output end Proof for 803327881190559997718960
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both funny and patient is strong. Everyone who is both not strong and wise is wise or not calm. If someone is creative then paul is not generous or not funny and vice versa. If john is either not curious or strong then susan is both not happy and not humble and vice versa. If someone is either happy or not quiet then lucy is both humble and calm and vice versa. Everyone who is either not wise or kind is both curious and old and vice versa. Everyone who is both generous and not curious is not rich and vice versa. Everyone who is tall or happy is not rich or quiet and vice versa. Everyone who is either not generous or funny is either curious or not tall and vice versa. Everyone who is both not brave and not kind is kind. Everyone who is either curious or not patient is either not quiet or not old. Everyone who is both wise and not curious is generous or not strong. Everyone who is not patient is humble and vice versa. Everyone who is brave or creative is either not quiet or not generous and vice versa. If john is quiet or kind then someone is quiet or not funny and vice versa. Everyone who is not strong or creative is generous or not patient. Susan is not generous. Someone is generous or creative. John is both not brave and not quiet. Lucy is not calm. Someone is both not tall and creative. Mary is not quiet. Someone is brave. John is either not generous or kind. | Lucy is brave. | neutral | (![X]:((funny(X)&patient(X))=>strong(X)))&
(![X]:((~strong(X)&wise(X))=>(wise(X)|~calm(X))))&
((?[X]:(creative(X)))<=>((~generous(paul)|~funny(paul))))&
(((~curious(john)<~>strong(john)))<=>((~happy(susan)&~humble(susan))))&
((?[X]:((happy(X)<~>~quiet(X))))<=>((humble(lucy)&calm(lucy))))&
(![X]:((~wise(X)<~>kind(X))<=>(curious(X)&old(X))))&
(![X]:((generous(X)&~curious(X))<=>~rich(X)))&
(![X]:((tall(X)|happy(X))<=>(~rich(X)|quiet(X))))&
(![X]:((~generous(X)<~>funny(X))<=>(curious(X)<~>~tall(X))))&
(![X]:((~brave(X)&~kind(X))=>kind(X)))&
(![X]:((curious(X)<~>~patient(X))=>(~quiet(X)<~>~old(X))))&
(![X]:((wise(X)&~curious(X))=>(generous(X)|~strong(X))))&
(![X]:(~patient(X)<=>humble(X)))&
(![X]:((brave(X)|creative(X))<=>(~quiet(X)<~>~generous(X))))&
(((quiet(john)|kind(john)))<=>(?[X]:((quiet(X)|~funny(X)))))&
(![X]:((~strong(X)|creative(X))=>(generous(X)|~patient(X))))&
(~generous(susan))&
(?[X]:((generous(X)|creative(X))))&
((~brave(john)&~quiet(john)))&
(~calm(lucy))&
(?[X]:((~tall(X)&creative(X))))&
(~quiet(mary))&
(?[X]:(brave(X)))&
((~generous(john)<~>kind(john))) | brave(lucy) | [] | null | 0 |
If paul is curious then someone is either tall or funny.
If susan is not quiet then fred is either not brave or not calm.
Everyone who is calm or rich is humble and vice versa.
Everyone who is not brave or calm is both not happy and funny.
Everyone who is both not generous and funny is happy or brave and vice versa.
If fred is not creative or quiet then someone is patient and vice versa.
Everyone who is generous is either not patient or rich and vice versa.
Everyone who is happy is not funny or not brave.
Everyone who is not humble is both not calm and happy and vice versa.
Everyone who is either not funny or curious is both not patient and strong and vice versa.
Everyone who is not brave is creative.
If someone is not rich then someone is both funny and not rich.
If someone is both not wise and happy then alice is either quiet or not patient and vice versa.
Everyone who is both quiet and generous is not humble or generous.
Everyone who is not kind is either strong or brave and vice versa.
Everyone who is not wise or not happy is both not wise and calm and vice versa.
Susan is either creative or not creative.
Alice is either kind or not humble.
Someone is not generous.
Someone is both creative and generous. | Paul is brave. | neutral | ((curious(paul))=>(?[X]:((tall(X)<~>funny(X)))))&
((~quiet(susan))=>((~brave(fred)<~>~calm(fred))))&
(![X]:((calm(X)|rich(X))<=>humble(X)))&
(![X]:((~brave(X)|calm(X))=>(~happy(X)&funny(X))))&
(![X]:((~generous(X)&funny(X))<=>(happy(X)|brave(X))))&
(((~creative(fred)|quiet(fred)))<=>(?[X]:(patient(X))))&
(![X]:(generous(X)<=>(~patient(X)<~>rich(X))))&
(![X]:(happy(X)=>(~funny(X)|~brave(X))))&
(![X]:(~humble(X)<=>(~calm(X)&happy(X))))&
(![X]:((~funny(X)<~>curious(X))<=>(~patient(X)&strong(X))))&
(![X]:(~brave(X)=>creative(X)))&
((?[X]:(~rich(X)))=>(?[X]:((funny(X)&~rich(X)))))&
((?[X]:((~wise(X)&happy(X))))<=>((quiet(alice)<~>~patient(alice))))&
(![X]:((quiet(X)&generous(X))=>(~humble(X)|generous(X))))&
(![X]:(~kind(X)<=>(strong(X)<~>brave(X))))&
(![X]:((~wise(X)|~happy(X))<=>(~wise(X)&calm(X))))&
((creative(susan)<~>~creative(susan)))&
((kind(alice)<~>~humble(alice)))&
(?[X]:(~generous(X)))&
(?[X]:((creative(X)&generous(X)))) | brave(paul) | [] | null | 0 |
Everyone who is either wise or not patient is either not calm or old and vice versa.
Everyone who is both funny and tall is both not funny and happy and vice versa.
Everyone who is both brave and kind is old and vice versa.
If john is both brave and curious then mary is creative.
If john is wise or not quiet then lucy is quiet.
Everyone who is strong or not old is either humble or not rich.
Everyone who is old or not funny is not tall.
If someone is both not creative and quiet then someone is patient or brave.
Everyone who is not generous or rich is either generous or not quiet.
Everyone who is brave or tall is either calm or patient.
If mary is both wise and humble then someone is either creative or not strong and vice versa.
If mary is either not generous or quiet then someone is kind or not humble.
Everyone who is either wise or not funny is not curious.
If john is either not old or kind then someone is not generous or not brave and vice versa.
If someone is not strong then someone is both tall and not curious.
If someone is not patient or not old then someone is both not kind and not strong and vice versa.
Alice is either not rich or not strong.
Someone is not creative.
Someone is either strong or not brave.
Fred is both not curious and not wise. | Alice is wise. | contradiction | (![X]:((wise(X)<~>~patient(X))<=>(~calm(X)<~>old(X))))&
(![X]:((funny(X)&tall(X))<=>(~funny(X)&happy(X))))&
(![X]:((brave(X)&kind(X))<=>old(X)))&
(((brave(john)&curious(john)))=>(creative(mary)))&
(((wise(john)|~quiet(john)))=>(quiet(lucy)))&
(![X]:((strong(X)|~old(X))=>(humble(X)<~>~rich(X))))&
(![X]:((old(X)|~funny(X))=>~tall(X)))&
((?[X]:((~creative(X)&quiet(X))))=>(?[X]:((patient(X)|brave(X)))))&
(![X]:((~generous(X)|rich(X))=>(generous(X)<~>~quiet(X))))&
(![X]:((brave(X)|tall(X))=>(calm(X)<~>patient(X))))&
(((wise(mary)&humble(mary)))<=>(?[X]:((creative(X)<~>~strong(X)))))&
(((~generous(mary)<~>quiet(mary)))=>(?[X]:((kind(X)|~humble(X)))))&
(![X]:((wise(X)<~>~funny(X))=>~curious(X)))&
(((~old(john)<~>kind(john)))<=>(?[X]:((~generous(X)|~brave(X)))))&
((?[X]:(~strong(X)))=>(?[X]:((tall(X)&~curious(X)))))&
((?[X]:((~patient(X)|~old(X))))<=>(?[X]:((~kind(X)&~strong(X)))))&
((~rich(alice)<~>~strong(alice)))&
(?[X]:(~creative(X)))&
(?[X]:((strong(X)<~>~brave(X))))&
((~curious(fred)&~wise(fred))) | wise(alice) | [
"p0",
"p1",
"p2",
"p6",
"p9",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 8463715634059183168262303
% SZS output start Proof for 8463715634059183168262303
1. ! [X0] : ((wise(X0) <~> ~patient(X0)) <=> (~calm(X0) <~> old(X0))) [input p0]
2. ! [X0] : ((tall(X0) & funny(X0)) <=> (happy(X0) & ~funny(X0))) [input p1]
3. ! [X0] : ((kind(X0) & brave(X0)) <=> old(X0)) [input p2]
7. ! [X0] : ((~funny(X0) | old(X0)) => ~tall(X0)) [input p6]
10. ! [X0] : ((tall(X0) | brave(X0)) => (calm(X0) <~> patient(X0))) [input p9]
15. ? [X0] : ~strong(X0) => ? [X0] : (~curious(X0) & tall(X0)) [input p14]
16. ? [X0] : (~old(X0) | ~patient(X0)) <=> ? [X0] : (~strong(X0) & ~kind(X0)) [input p15]
21. wise(alice) [input hypothesis]
23. ? [X0] : ~strong(X0) => ? [X1] : (~curious(X1) & tall(X1)) [rectify 15]
24. ? [X0] : (~old(X0) | ~patient(X0)) <=> ? [X1] : (~strong(X1) & ~kind(X1)) [rectify 16]
26. ? [X0] : ~strong(X0) => ? [X1] : tall(X1) [pure predicate removal 23]
31. ! [X0] : (~tall(X0) | (funny(X0) & ~old(X0))) [ennf transformation 7]
34. ! [X0] : ((calm(X0) <~> patient(X0)) | (~tall(X0) & ~brave(X0))) [ennf transformation 10]
36. ? [X1] : tall(X1) | ! [X0] : strong(X0) [ennf transformation 26]
37. ! [X0] : ((((patient(X0) | ~wise(X0)) & (~patient(X0) | wise(X0))) | ((~calm(X0) | ~old(X0)) & (old(X0) | calm(X0)))) & (((~old(X0) | calm(X0)) & (old(X0) | ~calm(X0))) | ((wise(X0) | patient(X0)) & (~patient(X0) | ~wise(X0))))) [nnf transformation 1]
38. ! [X0] : (((tall(X0) & funny(X0)) | (~happy(X0) | funny(X0))) & ((happy(X0) & ~funny(X0)) | (~tall(X0) | ~funny(X0)))) [nnf transformation 2]
39. ! [X0] : (((tall(X0) & funny(X0)) | ~happy(X0) | funny(X0)) & ((happy(X0) & ~funny(X0)) | ~tall(X0) | ~funny(X0))) [flattening 38]
40. ! [X0] : (((kind(X0) & brave(X0)) | ~old(X0)) & (old(X0) | (~kind(X0) | ~brave(X0)))) [nnf transformation 3]
41. ! [X0] : (((kind(X0) & brave(X0)) | ~old(X0)) & (old(X0) | ~kind(X0) | ~brave(X0))) [flattening 40]
47. ! [X0] : (((~patient(X0) | ~calm(X0)) & (patient(X0) | calm(X0))) | (~tall(X0) & ~brave(X0))) [nnf transformation 34]
60. ? [X0] : tall(X0) | ! [X1] : strong(X1) [rectify 36]
61. ? [X0] : tall(X0) => tall(sK4) [choice axiom]
62. tall(sK4) | ! [X1] : strong(X1) [skolemisation 60,61]
63. (? [X0] : (~old(X0) | ~patient(X0)) | ! [X1] : (strong(X1) | kind(X1))) & (? [X1] : (~strong(X1) & ~kind(X1)) | ! [X0] : (old(X0) & patient(X0))) [nnf transformation 24]
64. (? [X0] : (~old(X0) | ~patient(X0)) | ! [X1] : (strong(X1) | kind(X1))) & (? [X2] : (~strong(X2) & ~kind(X2)) | ! [X3] : (old(X3) & patient(X3))) [rectify 63]
65. ? [X0] : (~old(X0) | ~patient(X0)) => (~old(sK5) | ~patient(sK5)) [choice axiom]
66. ? [X2] : (~strong(X2) & ~kind(X2)) => (~strong(sK6) & ~kind(sK6)) [choice axiom]
67. ((~old(sK5) | ~patient(sK5)) | ! [X1] : (strong(X1) | kind(X1))) & ((~strong(sK6) & ~kind(sK6)) | ! [X3] : (old(X3) & patient(X3))) [skolemisation 64,66,65]
76. ~old(X0) | calm(X0) | ~patient(X0) | ~wise(X0) [cnf transformation 37]
82. ~funny(X0) | ~tall(X0) | ~funny(X0) [cnf transformation 39]
87. ~old(X0) | brave(X0) [cnf transformation 41]
96. ~tall(X0) | funny(X0) [cnf transformation 31]
104. ~brave(X0) | ~calm(X0) | ~patient(X0) [cnf transformation 47]
120. tall(sK4) | strong(X1) [cnf transformation 62]
123. ~strong(sK6) | patient(X3) [cnf transformation 67]
124. ~strong(sK6) | old(X3) [cnf transformation 67]
132. wise(alice) [cnf transformation 21]
134. ~tall(X0) | ~funny(X0) [duplicate literal removal 82]
150. ~tall(X0) [subsumption resolution 96,134]
212. 17 <=> ! [X0] : brave(X0) [avatar definition]
213. brave(X0) <- (17) [avatar component clause 212]
239. strong(X1) [subsumption resolution 120,150]
240. old(X3) [subsumption resolution 124,239]
241. patient(X3) [subsumption resolution 123,239]
248. brave(X0) [resolution 87,240]
249. 17 [avatar split clause 248,212]
261. ~calm(X0) | ~patient(X0) <- (17) [resolution 104,213]
263. ~calm(X0) <- (17) [subsumption resolution 261,241]
264. calm(X0) | ~patient(X0) | ~wise(X0) [resolution 76,240]
265. ~patient(X0) | ~wise(X0) <- (17) [subsumption resolution 264,263]
266. ~wise(X0) <- (17) [subsumption resolution 265,241]
267. $false <- (17) [resolution 266,132]
268. ~17 [avatar contradiction clause 267]
269. $false [avatar sat refutation 249,268]
% SZS output end Proof for 8463715634059183168262303
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both kind and patient is either curious or not rich.
Everyone who is not curious is not patient or not humble and vice versa.
If lucy is either rich or brave then someone is both funny and not old.
If alice is either funny or not tall then fred is either brave or not tall and vice versa.
If someone is not rich then paul is both not quiet and creative and vice versa.
If someone is not happy or not generous then someone is old or not tall.
If someone is strong or funny then john is both not old and not tall.
Everyone who is either quiet or happy is patient and vice versa.
Everyone who is patient or not old is either not funny or not strong.
Everyone who is quiet or wise is happy and vice versa.
Everyone who is both not curious and happy is not rich.
If someone is either calm or curious then someone is either funny or not curious and vice versa.
Everyone who is calm or not brave is both not humble and not quiet and vice versa.
Everyone who is both tall and kind is kind and vice versa.
Everyone who is both brave and calm is not humble or not wise.
Everyone who is either not patient or quiet is both kind and quiet and vice versa.
Mary is both not patient and not creative.
Someone is creative.
Someone is curious.
Someone is both calm and not humble.
Mary is happy or calm.
Someone is not rich or not calm.
Someone is not happy or not patient.
Someone is not funny or happy. | Paul is not happy. | contradiction | (![X]:((kind(X)&patient(X))=>(curious(X)<~>~rich(X))))&
(![X]:(~curious(X)<=>(~patient(X)|~humble(X))))&
(((rich(lucy)<~>brave(lucy)))=>(?[X]:((funny(X)&~old(X)))))&
(((funny(alice)<~>~tall(alice)))<=>((brave(fred)<~>~tall(fred))))&
((?[X]:(~rich(X)))<=>((~quiet(paul)&creative(paul))))&
((?[X]:((~happy(X)|~generous(X))))=>(?[X]:((old(X)|~tall(X)))))&
((?[X]:((strong(X)|funny(X))))=>((~old(john)&~tall(john))))&
(![X]:((quiet(X)<~>happy(X))<=>patient(X)))&
(![X]:((patient(X)|~old(X))=>(~funny(X)<~>~strong(X))))&
(![X]:((quiet(X)|wise(X))<=>happy(X)))&
(![X]:((~curious(X)&happy(X))=>~rich(X)))&
((?[X]:((calm(X)<~>curious(X))))<=>(?[X]:((funny(X)<~>~curious(X)))))&
(![X]:((calm(X)|~brave(X))<=>(~humble(X)&~quiet(X))))&
(![X]:((tall(X)&kind(X))<=>kind(X)))&
(![X]:((brave(X)&calm(X))=>(~humble(X)|~wise(X))))&
(![X]:((~patient(X)<~>quiet(X))<=>(kind(X)&quiet(X))))&
((~patient(mary)&~creative(mary)))&
(?[X]:(creative(X)))&
(?[X]:(curious(X)))&
(?[X]:((calm(X)&~humble(X))))&
((happy(mary)|calm(mary)))&
(?[X]:((~rich(X)|~calm(X))))&
(?[X]:((~happy(X)|~patient(X))))&
(?[X]:((~funny(X)|happy(X)))) | ~happy(paul) | [
"p7",
"p9",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 1044094745792173163340860
% SZS output start Proof for 1044094745792173163340860
8. ! [X0] : ((quiet(X0) <~> happy(X0)) <=> patient(X0)) [input p7]
10. ! [X0] : ((wise(X0) | quiet(X0)) <=> happy(X0)) [input p9]
16. ! [X0] : ((~patient(X0) <~> quiet(X0)) <=> (quiet(X0) & kind(X0))) [input p15]
25. ~happy(paul) [input hypothesis]
54. ! [X0] : ((((~happy(X0) | ~quiet(X0)) & (happy(X0) | quiet(X0))) | ~patient(X0)) & (patient(X0) | ((quiet(X0) | ~happy(X0)) & (happy(X0) | ~quiet(X0))))) [nnf transformation 8]
56. ! [X0] : (((wise(X0) | quiet(X0)) | ~happy(X0)) & (happy(X0) | (~wise(X0) & ~quiet(X0)))) [nnf transformation 10]
57. ! [X0] : ((wise(X0) | quiet(X0) | ~happy(X0)) & (happy(X0) | (~wise(X0) & ~quiet(X0)))) [flattening 56]
67. ! [X0] : ((((~quiet(X0) | patient(X0)) & (quiet(X0) | ~patient(X0))) | (~quiet(X0) | ~kind(X0))) & ((quiet(X0) & kind(X0)) | ((~patient(X0) | ~quiet(X0)) & (quiet(X0) | patient(X0))))) [nnf transformation 16]
68. ! [X0] : ((((~quiet(X0) | patient(X0)) & (quiet(X0) | ~patient(X0))) | ~quiet(X0) | ~kind(X0)) & ((quiet(X0) & kind(X0)) | ((~patient(X0) | ~quiet(X0)) & (quiet(X0) | patient(X0))))) [flattening 67]
108. ~patient(X0) | quiet(X0) | happy(X0) [cnf transformation 54]
114. ~quiet(X0) | happy(X0) [cnf transformation 57]
137. quiet(X0) | quiet(X0) | patient(X0) [cnf transformation 68]
151. ~happy(paul) [cnf transformation 25]
152. quiet(X0) | patient(X0) [duplicate literal removal 137]
199. 9 <=> quiet(paul) [avatar definition]
200. ~quiet(paul) <- (~9) [avatar component clause 199]
201. quiet(paul) <- (9) [avatar component clause 199]
327. patient(paul) <- (~9) [resolution 152,200]
334. quiet(paul) | happy(paul) <- (~9) [resolution 108,327]
338. happy(paul) <- (~9) [subsumption resolution 334,200]
339. $false <- (~9) [subsumption resolution 338,151]
340. 9 [avatar contradiction clause 339]
346. happy(paul) <- (9) [resolution 201,114]
347. $false <- (9) [subsumption resolution 346,151]
348. ~9 [avatar contradiction clause 347]
349. $false [avatar sat refutation 340,348]
% SZS output end Proof for 1044094745792173163340860
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not humble and not calm is funny and vice versa. If someone is not calm or kind then someone is old. Everyone who is either calm or not wise is both not calm and kind and vice versa. If someone is generous then alice is both curious and rich and vice versa. If someone is both not brave and kind then someone is not curious or not generous and vice versa. If someone is not kind or strong then someone is both not old and not creative. Everyone who is calm is patient or not happy. Everyone who is patient is not wise or not old and vice versa. Everyone who is either not rich or rich is not patient or strong and vice versa. Everyone who is either creative or curious is humble or not quiet. If someone is either humble or not kind then alice is not wise or wise and vice versa. Everyone who is both funny and rich is either not quiet or not patient and vice versa. Everyone who is tall or not generous is not calm or creative. Everyone who is not strong is not quiet and vice versa. If someone is either generous or not humble then susan is not old and vice versa. Everyone who is either happy or funny is curious or happy and vice versa. Someone is both happy and patient. Someone is either wise or not brave. Someone is both tall and not funny. Susan is not generous or happy. Someone is either not patient or not humble. Someone is both patient and kind. Paul is both old and tall. Someone is both not funny and brave. | Susan is funny. | neutral | (![X]:((~humble(X)&~calm(X))<=>funny(X)))&
((?[X]:((~calm(X)|kind(X))))=>(?[X]:(old(X))))&
(![X]:((calm(X)<~>~wise(X))<=>(~calm(X)&kind(X))))&
((?[X]:(generous(X)))<=>((curious(alice)&rich(alice))))&
((?[X]:((~brave(X)&kind(X))))<=>(?[X]:((~curious(X)|~generous(X)))))&
((?[X]:((~kind(X)|strong(X))))=>(?[X]:((~old(X)&~creative(X)))))&
(![X]:(calm(X)=>(patient(X)|~happy(X))))&
(![X]:(patient(X)<=>(~wise(X)|~old(X))))&
(![X]:((~rich(X)<~>rich(X))<=>(~patient(X)|strong(X))))&
(![X]:((creative(X)<~>curious(X))=>(humble(X)|~quiet(X))))&
((?[X]:((humble(X)<~>~kind(X))))<=>((~wise(alice)|wise(alice))))&
(![X]:((funny(X)&rich(X))<=>(~quiet(X)<~>~patient(X))))&
(![X]:((tall(X)|~generous(X))=>(~calm(X)|creative(X))))&
(![X]:(~strong(X)<=>~quiet(X)))&
((?[X]:((generous(X)<~>~humble(X))))<=>(~old(susan)))&
(![X]:((happy(X)<~>funny(X))<=>(curious(X)|happy(X))))&
(?[X]:((happy(X)&patient(X))))&
(?[X]:((wise(X)<~>~brave(X))))&
(?[X]:((tall(X)&~funny(X))))&
((~generous(susan)|happy(susan)))&
(?[X]:((~patient(X)<~>~humble(X))))&
(?[X]:((patient(X)&kind(X))))&
((old(paul)&tall(paul)))&
(?[X]:((~funny(X)&brave(X)))) | funny(susan) | [] | null | 0 |
Everyone who is generous or not patient is old.
If paul is not patient or tall then someone is creative.
If someone is both funny and not creative then fred is both not happy and not calm and vice versa.
Everyone who is not generous or happy is either brave or funny and vice versa.
Everyone who is kind or not brave is both kind and calm.
If susan is either not creative or creative then fred is either brave or patient and vice versa.
Everyone who is both brave and not brave is either quiet or not humble.
Everyone who is either brave or not old is either kind or generous and vice versa.
Everyone who is generous is not quiet.
Everyone who is not humble is quiet or not brave and vice versa.
Everyone who is not strong is either tall or humble and vice versa.
Everyone who is not rich is curious or not kind.
Everyone who is rich is not old.
Everyone who is funny or not curious is both not old and generous.
If john is either not funny or not kind then someone is generous or humble and vice versa.
If paul is funny or not happy then someone is both happy and brave.
Paul is not wise.
Someone is rich or not rich.
Someone is either not rich or not quiet.
Fred is both not humble and happy.
Someone is either not tall or brave.
Someone is either not happy or not brave.
Paul is either not curious or creative. | Fred is quiet. | entailment | (![X]:((generous(X)|~patient(X))=>old(X)))&
(((~patient(paul)|tall(paul)))=>(?[X]:(creative(X))))&
((?[X]:((funny(X)&~creative(X))))<=>((~happy(fred)&~calm(fred))))&
(![X]:((~generous(X)|happy(X))<=>(brave(X)<~>funny(X))))&
(![X]:((kind(X)|~brave(X))=>(kind(X)&calm(X))))&
(((~creative(susan)<~>creative(susan)))<=>((brave(fred)<~>patient(fred))))&
(![X]:((brave(X)&~brave(X))=>(quiet(X)<~>~humble(X))))&
(![X]:((brave(X)<~>~old(X))<=>(kind(X)<~>generous(X))))&
(![X]:(generous(X)=>~quiet(X)))&
(![X]:(~humble(X)<=>(quiet(X)|~brave(X))))&
(![X]:(~strong(X)<=>(tall(X)<~>humble(X))))&
(![X]:(~rich(X)=>(curious(X)|~kind(X))))&
(![X]:(rich(X)=>~old(X)))&
(![X]:((funny(X)|~curious(X))=>(~old(X)&generous(X))))&
(((~funny(john)<~>~kind(john)))<=>(?[X]:((generous(X)|humble(X)))))&
(((funny(paul)|~happy(paul)))=>(?[X]:((happy(X)&brave(X)))))&
(~wise(paul))&
(?[X]:((rich(X)|~rich(X))))&
(?[X]:((~rich(X)<~>~quiet(X))))&
((~humble(fred)&happy(fred)))&
(?[X]:((~tall(X)<~>brave(X))))&
(?[X]:((~happy(X)<~>~brave(X))))&
((~curious(paul)<~>creative(paul))) | quiet(fred) | [
"p0",
"p3",
"p9",
"p13",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 655330257168718021535013
% SZS output start Proof for 655330257168718021535013
1. ! [X0] : ((~patient(X0) | generous(X0)) => old(X0)) [input p0]
4. ! [X0] : ((happy(X0) | ~generous(X0)) <=> (brave(X0) <~> funny(X0))) [input p3]
10. ! [X0] : (~humble(X0) <=> (~brave(X0) | quiet(X0))) [input p9]
14. ! [X0] : ((~curious(X0) | funny(X0)) => (generous(X0) & ~old(X0))) [input p13]
20. happy(fred) & ~humble(fred) [input p19]
24. ~quiet(fred) [input hypothesis]
26. ! [X0] : (old(X0) | (patient(X0) & ~generous(X0))) [ennf transformation 1]
35. ! [X0] : ((generous(X0) & ~old(X0)) | (curious(X0) & ~funny(X0))) [ennf transformation 14]
44. ! [X0] : (((happy(X0) | ~generous(X0)) | ((brave(X0) | ~funny(X0)) & (funny(X0) | ~brave(X0)))) & (((~funny(X0) | ~brave(X0)) & (funny(X0) | brave(X0))) | (~happy(X0) & generous(X0)))) [nnf transformation 4]
45. ! [X0] : ((happy(X0) | ~generous(X0) | ((brave(X0) | ~funny(X0)) & (funny(X0) | ~brave(X0)))) & (((~funny(X0) | ~brave(X0)) & (funny(X0) | brave(X0))) | (~happy(X0) & generous(X0)))) [flattening 44]
49. ! [X0] : ((~humble(X0) | (brave(X0) & ~quiet(X0))) & ((~brave(X0) | quiet(X0)) | humble(X0))) [nnf transformation 10]
50. ! [X0] : ((~humble(X0) | (brave(X0) & ~quiet(X0))) & (~brave(X0) | quiet(X0) | humble(X0))) [flattening 49]
69. ~generous(X0) | old(X0) [cnf transformation 26]
78. ~happy(X0) | brave(X0) | funny(X0) [cnf transformation 45]
106. ~brave(X0) | quiet(X0) | humble(X0) [cnf transformation 50]
111. ~funny(X0) | ~old(X0) [cnf transformation 35]
113. ~funny(X0) | generous(X0) [cnf transformation 35]
128. ~humble(fred) [cnf transformation 20]
129. happy(fred) [cnf transformation 20]
136. ~quiet(fred) [cnf transformation 24]
156. 4 <=> happy(fred) [avatar definition]
158. happy(fred) <- (4) [avatar component clause 156]
183. 10 <=> brave(fred) [avatar definition]
184. brave(fred) <- (10) [avatar component clause 183]
256. 4 [avatar split clause 129,156]
306. brave(fred) | funny(fred) <- (4) [resolution 78,158]
343. quiet(fred) | humble(fred) <- (10) [resolution 106,184]
351. humble(fred) <- (10) [subsumption resolution 343,136]
352. $false <- (10) [subsumption resolution 351,128]
353. ~10 [avatar contradiction clause 352]
358. 32 <=> funny(fred) [avatar definition]
360. funny(fred) <- (32) [avatar component clause 358]
361. 32 | 10 | ~4 [avatar split clause 306,156,183,358]
373. generous(fred) <- (32) [resolution 360,113]
374. ~old(fred) <- (32) [resolution 360,111]
491. old(fred) <- (32) [resolution 373,69]
492. $false <- (32) [subsumption resolution 491,374]
493. ~32 [avatar contradiction clause 492]
494. $false [avatar sat refutation 256,353,361,493]
% SZS output end Proof for 655330257168718021535013
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If fred is both generous and not wise then susan is both not happy and not patient and vice versa. If susan is both not curious and not tall then someone is funny or not creative. If someone is not strong then someone is generous or wise and vice versa. Everyone who is not funny is either not rich or not calm and vice versa. Everyone who is not old or not patient is not strong. If alice is either not generous or not wise then someone is either tall or brave and vice versa. Everyone who is curious is both not strong and not funny. If fred is not strong or happy then john is happy or not kind and vice versa. Everyone who is funny or generous is curious or rich. If someone is wise then mary is both kind and strong. If fred is either not patient or happy then alice is either brave or quiet. Everyone who is curious is funny. Everyone who is not calm or not brave is both not patient and humble and vice versa. If someone is funny then someone is either not humble or old and vice versa. If someone is strong or wise then fred is both not funny and not patient and vice versa. Everyone who is not funny or strong is either calm or not curious. Someone is either curious or creative. Someone is not calm or creative. Paul is either not curious or not humble. Alice is happy or not old. Alice is either brave or kind. John is either not happy or not quiet. | Paul is strong. | contradiction | (((generous(fred)&~wise(fred)))<=>((~happy(susan)&~patient(susan))))&
(((~curious(susan)&~tall(susan)))=>(?[X]:((funny(X)|~creative(X)))))&
((?[X]:(~strong(X)))<=>(?[X]:((generous(X)|wise(X)))))&
(![X]:(~funny(X)<=>(~rich(X)<~>~calm(X))))&
(![X]:((~old(X)|~patient(X))=>~strong(X)))&
(((~generous(alice)<~>~wise(alice)))<=>(?[X]:((tall(X)<~>brave(X)))))&
(![X]:(curious(X)=>(~strong(X)&~funny(X))))&
(((~strong(fred)|happy(fred)))<=>((happy(john)|~kind(john))))&
(![X]:((funny(X)|generous(X))=>(curious(X)|rich(X))))&
((?[X]:(wise(X)))=>((kind(mary)&strong(mary))))&
(((~patient(fred)<~>happy(fred)))=>((brave(alice)<~>quiet(alice))))&
(![X]:(curious(X)=>funny(X)))&
(![X]:((~calm(X)|~brave(X))<=>(~patient(X)&humble(X))))&
((?[X]:(funny(X)))<=>(?[X]:((~humble(X)<~>old(X)))))&
((?[X]:((strong(X)|wise(X))))<=>((~funny(fred)&~patient(fred))))&
(![X]:((~funny(X)|strong(X))=>(calm(X)<~>~curious(X))))&
(?[X]:((curious(X)<~>creative(X))))&
(?[X]:((~calm(X)|creative(X))))&
((~curious(paul)<~>~humble(paul)))&
((happy(alice)|~old(alice)))&
((brave(alice)<~>kind(alice)))&
((~happy(john)<~>~quiet(john))) | strong(paul) | [
"p4",
"p6",
"p11",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 4043793897055109654647460
% SZS output start Proof for 4043793897055109654647460
5. ! [X0] : ((~patient(X0) | ~old(X0)) => ~strong(X0)) [input p4]
7. ! [X0] : (curious(X0) => (~funny(X0) & ~strong(X0))) [input p6]
12. ! [X0] : (curious(X0) => funny(X0)) [input p11]
13. ! [X0] : ((~brave(X0) | ~calm(X0)) <=> (humble(X0) & ~patient(X0))) [input p12]
16. ! [X0] : ((strong(X0) | ~funny(X0)) => (calm(X0) <~> ~curious(X0))) [input p15]
23. strong(paul) [input hypothesis]
28. ! [X0] : (~strong(X0) | (patient(X0) & old(X0))) [ennf transformation 5]
29. ! [X0] : ((~funny(X0) & ~strong(X0)) | ~curious(X0)) [ennf transformation 7]
34. ! [X0] : (funny(X0) | ~curious(X0)) [ennf transformation 12]
35. ! [X0] : ((calm(X0) <~> ~curious(X0)) | (~strong(X0) & funny(X0))) [ennf transformation 16]
53. ! [X0] : (((~brave(X0) | ~calm(X0)) | (~humble(X0) | patient(X0))) & ((humble(X0) & ~patient(X0)) | (brave(X0) & calm(X0)))) [nnf transformation 13]
54. ! [X0] : ((~brave(X0) | ~calm(X0) | ~humble(X0) | patient(X0)) & ((humble(X0) & ~patient(X0)) | (brave(X0) & calm(X0)))) [flattening 53]
65. ! [X0] : (((curious(X0) | ~calm(X0)) & (~curious(X0) | calm(X0))) | (~strong(X0) & funny(X0))) [nnf transformation 35]
87. ~strong(X0) | patient(X0) [cnf transformation 28]
97. ~funny(X0) | ~curious(X0) [cnf transformation 29]
110. funny(X0) | ~curious(X0) [cnf transformation 34]
111. ~patient(X0) | calm(X0) [cnf transformation 54]
128. curious(X0) | ~calm(X0) | ~strong(X0) [cnf transformation 65]
139. strong(paul) [cnf transformation 23]
278. ~curious(X0) [subsumption resolution 110,97]
324. ~calm(X0) | ~strong(X0) [subsumption resolution 128,278]
362. patient(paul) [resolution 87,139]
367. calm(paul) [resolution 111,362]
377. ~strong(paul) [resolution 324,367]
380. $false [subsumption resolution 377,139]
% SZS output end Proof for 4043793897055109654647460
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If fred is either not rich or old then someone is both tall and rich and vice versa.
If someone is either happy or not quiet then susan is not curious or happy and vice versa.
Everyone who is both curious and not creative is not rich or old and vice versa.
If someone is either not creative or not old then someone is not humble and vice versa.
If someone is both creative and not old then someone is both not curious and not tall and vice versa.
Everyone who is either not strong or not curious is calm or not calm and vice versa.
If someone is not rich or not old then someone is either rich or not calm.
Everyone who is not rich is not calm or humble.
Everyone who is either funny or not quiet is not quiet.
If alice is either not tall or not generous then someone is not happy or not quiet and vice versa.
Everyone who is funny or humble is either not quiet or tall.
If paul is not old or generous then someone is old.
If someone is not wise then someone is not tall or generous.
Everyone who is not strong is both rich and tall.
Everyone who is not old or not funny is not wise or brave and vice versa.
Someone is not creative or calm.
Someone is not strong or happy.
Someone is both rich and not old.
Someone is both not brave and not quiet.
Someone is both happy and curious.
Someone is creative or not patient.
Mary is not rich or happy.
Someone is curious. | Fred is not curious. | contradiction | (((~rich(fred)<~>old(fred)))<=>(?[X]:((tall(X)&rich(X)))))&
((?[X]:((happy(X)<~>~quiet(X))))<=>((~curious(susan)|happy(susan))))&
(![X]:((curious(X)&~creative(X))<=>(~rich(X)|old(X))))&
((?[X]:((~creative(X)<~>~old(X))))<=>(?[X]:(~humble(X))))&
((?[X]:((creative(X)&~old(X))))<=>(?[X]:((~curious(X)&~tall(X)))))&
(![X]:((~strong(X)<~>~curious(X))<=>(calm(X)|~calm(X))))&
((?[X]:((~rich(X)|~old(X))))=>(?[X]:((rich(X)<~>~calm(X)))))&
(![X]:(~rich(X)=>(~calm(X)|humble(X))))&
(![X]:((funny(X)<~>~quiet(X))=>~quiet(X)))&
(((~tall(alice)<~>~generous(alice)))<=>(?[X]:((~happy(X)|~quiet(X)))))&
(![X]:((funny(X)|humble(X))=>(~quiet(X)<~>tall(X))))&
(((~old(paul)|generous(paul)))=>(?[X]:(old(X))))&
((?[X]:(~wise(X)))=>(?[X]:((~tall(X)|generous(X)))))&
(![X]:(~strong(X)=>(rich(X)&tall(X))))&
(![X]:((~old(X)|~funny(X))<=>(~wise(X)|brave(X))))&
(?[X]:((~creative(X)|calm(X))))&
(?[X]:((~strong(X)|happy(X))))&
(?[X]:((rich(X)&~old(X))))&
(?[X]:((~brave(X)&~quiet(X))))&
(?[X]:((happy(X)&curious(X))))&
(?[X]:((creative(X)|~patient(X))))&
((~rich(mary)|happy(mary)))&
(?[X]:(curious(X))) | ~curious(fred) | [
"p0",
"p2",
"p5",
"p13",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 5245471595612424327150218
% SZS output start Proof for 5245471595612424327150218
1. (~rich(fred) <~> old(fred)) <=> ? [X0] : (rich(X0) & tall(X0)) [input p0]
3. ! [X0] : ((~creative(X0) & curious(X0)) <=> (old(X0) | ~rich(X0))) [input p2]
6. ! [X0] : ((~strong(X0) <~> ~curious(X0)) <=> (~calm(X0) | calm(X0))) [input p5]
14. ! [X0] : (~strong(X0) => (tall(X0) & rich(X0))) [input p13]
20. ? [X0] : (curious(X0) & happy(X0)) [input p19]
24. ~curious(fred) [input hypothesis]
37. ! [X0] : ((tall(X0) & rich(X0)) | strong(X0)) [ennf transformation 14]
38. (((~old(fred) | rich(fred)) & (old(fred) | ~rich(fred))) | ! [X0] : (~rich(X0) | ~tall(X0))) & (? [X0] : (rich(X0) & tall(X0)) | ((~rich(fred) | ~old(fred)) & (old(fred) | rich(fred)))) [nnf transformation 1]
39. (((~old(fred) | rich(fred)) & (old(fred) | ~rich(fred))) | ! [X0] : (~rich(X0) | ~tall(X0))) & (? [X1] : (rich(X1) & tall(X1)) | ((~rich(fred) | ~old(fred)) & (old(fred) | rich(fred)))) [rectify 38]
40. ? [X1] : (rich(X1) & tall(X1)) => (rich(sK0) & tall(sK0)) [choice axiom]
41. (((~old(fred) | rich(fred)) & (old(fred) | ~rich(fred))) | ! [X0] : (~rich(X0) | ~tall(X0))) & ((rich(sK0) & tall(sK0)) | ((~rich(fred) | ~old(fred)) & (old(fred) | rich(fred)))) [skolemisation 39,40]
47. ! [X0] : (((~creative(X0) & curious(X0)) | (~old(X0) & rich(X0))) & ((old(X0) | ~rich(X0)) | (creative(X0) | ~curious(X0)))) [nnf transformation 3]
48. ! [X0] : (((~creative(X0) & curious(X0)) | (~old(X0) & rich(X0))) & (old(X0) | ~rich(X0) | creative(X0) | ~curious(X0))) [flattening 47]
59. ! [X0] : ((((curious(X0) | strong(X0)) & (~curious(X0) | ~strong(X0))) | (calm(X0) & ~calm(X0))) & ((~calm(X0) | calm(X0)) | ((~strong(X0) | curious(X0)) & (~curious(X0) | strong(X0))))) [nnf transformation 6]
60. ! [X0] : ((((curious(X0) | strong(X0)) & (~curious(X0) | ~strong(X0))) | (calm(X0) & ~calm(X0))) & (~calm(X0) | calm(X0) | ((~strong(X0) | curious(X0)) & (~curious(X0) | strong(X0))))) [flattening 59]
86. ? [X0] : (curious(X0) & happy(X0)) => (curious(sK14) & happy(sK14)) [choice axiom]
87. curious(sK14) & happy(sK14) [skolemisation 20,86]
94. old(fred) | ~rich(fred) | ~rich(X0) | ~tall(X0) [cnf transformation 41]
103. curious(X0) | rich(X0) [cnf transformation 48]
104. ~old(X0) | curious(X0) [cnf transformation 48]
117. ~curious(X0) | ~strong(X0) | ~calm(X0) [cnf transformation 60]
118. ~strong(X0) | ~curious(X0) | calm(X0) [cnf transformation 60]
141. strong(X0) | rich(X0) [cnf transformation 37]
142. strong(X0) | tall(X0) [cnf transformation 37]
154. curious(sK14) [cnf transformation 87]
157. ~curious(fred) [cnf transformation 24]
160. 1 <=> ! [X0] : (~rich(X0) | ~tall(X0)) [avatar definition]
161. ~tall(X0) | ~rich(X0) <- (1) [avatar component clause 160]
163. 2 <=> rich(fred) [avatar definition]
167. 3 <=> old(fred) [avatar definition]
168. old(fred) <- (3) [avatar component clause 167]
171. 1 | ~2 | 3 [avatar split clause 94,167,163,160]
264. ~strong(X0) | ~curious(X0) [subsumption resolution 117,118]
278. 26 <=> ! [X1] : rich(X1) [avatar definition]
279. rich(X1) <- (26) [avatar component clause 278]
369. rich(fred) [resolution 103,157]
374. 2 [avatar split clause 369,163]
377. curious(fred) <- (3) [resolution 104,168]
378. $false <- (3) [subsumption resolution 377,157]
379. ~3 [avatar contradiction clause 378]
399. ~curious(X1) | tall(X1) [resolution 264,142]
400. ~curious(X2) | rich(X2) [resolution 264,141]
402. rich(X2) [subsumption resolution 400,103]
403. 26 [avatar split clause 402,278]
428. tall(sK14) [resolution 399,154]
442. ~rich(sK14) <- (1) [resolution 428,161]
443. $false <- (1, 26) [subsumption resolution 442,279]
444. ~1 | ~26 [avatar contradiction clause 443]
445. $false [avatar sat refutation 171,374,379,403,444]
% SZS output end Proof for 5245471595612424327150218
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not old or not patient is both not old and not brave and vice versa. If someone is strong or not generous then fred is both not kind and calm and vice versa. Everyone who is brave or not happy is both kind and not calm. Everyone who is rich is wise or not tall. Everyone who is either not curious or not calm is curious and vice versa. Everyone who is both tall and not generous is either wise or not happy. Everyone who is not rich is both not calm and calm and vice versa. If someone is humble or brave then someone is not rich. If someone is not funny then lucy is brave. Everyone who is either not curious or humble is both not patient and tall. Everyone who is old is not kind. If someone is not creative or humble then john is both quiet and not strong and vice versa. If john is both creative and not happy then paul is not strong. If mary is brave or not strong then someone is either strong or not patient and vice versa. Everyone who is either quiet or calm is both not wise and funny and vice versa. If someone is both humble and curious then someone is either humble or not creative and vice versa. Fred is either not generous or old. Alice is either patient or rich. Lucy is both tall and not curious. Susan is either not wise or rich. Someone is not tall. | John is not wise. | contradiction | (![X]:((~old(X)|~patient(X))<=>(~old(X)&~brave(X))))&
((?[X]:((strong(X)|~generous(X))))<=>((~kind(fred)&calm(fred))))&
(![X]:((brave(X)|~happy(X))=>(kind(X)&~calm(X))))&
(![X]:(rich(X)=>(wise(X)|~tall(X))))&
(![X]:((~curious(X)<~>~calm(X))<=>curious(X)))&
(![X]:((tall(X)&~generous(X))=>(wise(X)<~>~happy(X))))&
(![X]:(~rich(X)<=>(~calm(X)&calm(X))))&
((?[X]:((humble(X)|brave(X))))=>(?[X]:(~rich(X))))&
((?[X]:(~funny(X)))=>(brave(lucy)))&
(![X]:((~curious(X)<~>humble(X))=>(~patient(X)&tall(X))))&
(![X]:(old(X)=>~kind(X)))&
((?[X]:((~creative(X)|humble(X))))<=>((quiet(john)&~strong(john))))&
(((creative(john)&~happy(john)))=>(~strong(paul)))&
(((brave(mary)|~strong(mary)))<=>(?[X]:((strong(X)<~>~patient(X)))))&
(![X]:((quiet(X)<~>calm(X))<=>(~wise(X)&funny(X))))&
((?[X]:((humble(X)&curious(X))))<=>(?[X]:((humble(X)<~>~creative(X)))))&
((~generous(fred)<~>old(fred)))&
((patient(alice)<~>rich(alice)))&
((tall(lucy)&~curious(lucy)))&
((~wise(susan)<~>rich(susan)))&
(?[X]:(~tall(X))) | ~wise(john) | [
"p1",
"p4",
"p6",
"p7",
"p8",
"p11",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 5098546574123742992368110
% SZS output start Proof for 5098546574123742992368110
2. ? [X0] : (~generous(X0) | strong(X0)) <=> (calm(fred) & ~kind(fred)) [input p1]
5. ! [X0] : ((~curious(X0) <~> ~calm(X0)) <=> curious(X0)) [input p4]
7. ! [X0] : (~rich(X0) <=> (calm(X0) & ~calm(X0))) [input p6]
8. ? [X0] : (brave(X0) | humble(X0)) => ? [X0] : ~rich(X0) [input p7]
9. ? [X0] : ~funny(X0) => brave(lucy) [input p8]
12. ? [X0] : (humble(X0) | ~creative(X0)) <=> (~strong(john) & quiet(john)) [input p11]
15. ! [X0] : ((quiet(X0) <~> calm(X0)) <=> (funny(X0) & ~wise(X0))) [input p14]
16. ? [X0] : (curious(X0) & humble(X0)) <=> ? [X0] : (humble(X0) <~> ~creative(X0)) [input p15]
22. ~wise(john) [input hypothesis]
23. ? [X0] : (brave(X0) | humble(X0)) => ? [X1] : ~rich(X1) [rectify 8]
24. ? [X0] : (curious(X0) & humble(X0)) <=> ? [X1] : (humble(X1) <~> ~creative(X1)) [rectify 16]
30. ? [X1] : ~rich(X1) | ! [X0] : (~brave(X0) & ~humble(X0)) [ennf transformation 23]
31. brave(lucy) | ! [X0] : funny(X0) [ennf transformation 9]
38. (? [X0] : (~generous(X0) | strong(X0)) | (~calm(fred) | kind(fred))) & ((calm(fred) & ~kind(fred)) | ! [X0] : (generous(X0) & ~strong(X0))) [nnf transformation 2]
39. (? [X0] : (~generous(X0) | strong(X0)) | ~calm(fred) | kind(fred)) & ((calm(fred) & ~kind(fred)) | ! [X0] : (generous(X0) & ~strong(X0))) [flattening 38]
40. (? [X0] : (~generous(X0) | strong(X0)) | ~calm(fred) | kind(fred)) & ((calm(fred) & ~kind(fred)) | ! [X1] : (generous(X1) & ~strong(X1))) [rectify 39]
41. ? [X0] : (~generous(X0) | strong(X0)) => (~generous(sK0) | strong(sK0)) [choice axiom]
42. ((~generous(sK0) | strong(sK0)) | ~calm(fred) | kind(fred)) & ((calm(fred) & ~kind(fred)) | ! [X1] : (generous(X1) & ~strong(X1))) [skolemisation 40,41]
43. ! [X0] : ((((calm(X0) | curious(X0)) & (~calm(X0) | ~curious(X0))) | ~curious(X0)) & (curious(X0) | ((~curious(X0) | calm(X0)) & (~calm(X0) | curious(X0))))) [nnf transformation 5]
45. ! [X0] : ((~rich(X0) | (~calm(X0) | calm(X0))) & ((calm(X0) & ~calm(X0)) | rich(X0))) [nnf transformation 7]
46. ! [X0] : ((~rich(X0) | ~calm(X0) | calm(X0)) & ((calm(X0) & ~calm(X0)) | rich(X0))) [flattening 45]
47. ? [X0] : ~rich(X0) | ! [X1] : (~brave(X1) & ~humble(X1)) [rectify 30]
48. ? [X0] : ~rich(X0) => ~rich(sK1) [choice axiom]
49. ~rich(sK1) | ! [X1] : (~brave(X1) & ~humble(X1)) [skolemisation 47,48]
51. (? [X0] : (humble(X0) | ~creative(X0)) | (strong(john) | ~quiet(john))) & ((~strong(john) & quiet(john)) | ! [X0] : (~humble(X0) & creative(X0))) [nnf transformation 12]
52. (? [X0] : (humble(X0) | ~creative(X0)) | strong(john) | ~quiet(john)) & ((~strong(john) & quiet(john)) | ! [X0] : (~humble(X0) & creative(X0))) [flattening 51]
53. (? [X0] : (humble(X0) | ~creative(X0)) | strong(john) | ~quiet(john)) & ((~strong(john) & quiet(john)) | ! [X1] : (~humble(X1) & creative(X1))) [rectify 52]
54. ? [X0] : (humble(X0) | ~creative(X0)) => (humble(sK2) | ~creative(sK2)) [choice axiom]
55. ((humble(sK2) | ~creative(sK2)) | strong(john) | ~quiet(john)) & ((~strong(john) & quiet(john)) | ! [X1] : (~humble(X1) & creative(X1))) [skolemisation 53,54]
61. ! [X0] : ((((~calm(X0) | ~quiet(X0)) & (calm(X0) | quiet(X0))) | (~funny(X0) | wise(X0))) & ((funny(X0) & ~wise(X0)) | ((quiet(X0) | ~calm(X0)) & (calm(X0) | ~quiet(X0))))) [nnf transformation 15]
62. ! [X0] : ((((~calm(X0) | ~quiet(X0)) & (calm(X0) | quiet(X0))) | ~funny(X0) | wise(X0)) & ((funny(X0) & ~wise(X0)) | ((quiet(X0) | ~calm(X0)) & (calm(X0) | ~quiet(X0))))) [flattening 61]
63. (? [X0] : (curious(X0) & humble(X0)) | ! [X1] : ((humble(X1) | creative(X1)) & (~creative(X1) | ~humble(X1)))) & (? [X1] : ((creative(X1) | ~humble(X1)) & (~creative(X1) | humble(X1))) | ! [X0] : (~curious(X0) | ~humble(X0))) [nnf transformation 24]
64. (? [X0] : (curious(X0) & humble(X0)) | ! [X1] : ((humble(X1) | creative(X1)) & (~creative(X1) | ~humble(X1)))) & (? [X2] : ((creative(X2) | ~humble(X2)) & (~creative(X2) | humble(X2))) | ! [X3] : (~curious(X3) | ~humble(X3))) [rectify 63]
65. ? [X0] : (curious(X0) & humble(X0)) => (curious(sK4) & humble(sK4)) [choice axiom]
66. ? [X2] : ((creative(X2) | ~humble(X2)) & (~creative(X2) | humble(X2))) => ((creative(sK5) | ~humble(sK5)) & (~creative(sK5) | humble(sK5))) [choice axiom]
67. ((curious(sK4) & humble(sK4)) | ! [X1] : ((humble(X1) | creative(X1)) & (~creative(X1) | ~humble(X1)))) & (((creative(sK5) | ~humble(sK5)) & (~creative(sK5) | humble(sK5))) | ! [X3] : (~curious(X3) | ~humble(X3))) [skolemisation 64,66,65]
80. calm(fred) | ~strong(X1) [cnf transformation 42]
88. curious(X0) | ~calm(X0) | curious(X0) [cnf transformation 43]
90. ~calm(X0) | ~curious(X0) | ~curious(X0) [cnf transformation 43]
95. calm(X0) | rich(X0) [cnf transformation 46]
97. ~rich(sK1) | ~humble(X1) [cnf transformation 49]
98. ~rich(sK1) | ~brave(X1) [cnf transformation 49]
99. brave(lucy) | funny(X0) [cnf transformation 31]
109. humble(sK2) | ~creative(sK2) | strong(john) | ~quiet(john) [cnf transformation 55]
121. calm(X0) | quiet(X0) | ~funny(X0) | wise(X0) [cnf transformation 62]
126. humble(sK4) | humble(X1) | creative(X1) [cnf transformation 67]
138. ~wise(john) [cnf transformation 22]
139. curious(X0) | ~calm(X0) [duplicate literal removal 88]
140. ~curious(X0) | ~calm(X0) [duplicate literal removal 90]
146. 2 <=> calm(fred) [avatar definition]
147. calm(fred) <- (2) [avatar component clause 146]
163. 6 <=> ! [X1] : ~strong(X1) [avatar definition]
164. ~strong(X1) <- (6) [avatar component clause 163]
165. 6 | 2 [avatar split clause 80,146,163]
168. ~calm(X0) [subsumption resolution 139,140]
169. rich(X0) [subsumption resolution 95,168]
170. ~brave(X1) [subsumption resolution 98,169]
171. ~humble(X1) [subsumption resolution 97,169]
172. funny(X0) [subsumption resolution 99,170]
175. ~creative(sK2) | strong(john) | ~quiet(john) [subsumption resolution 109,171]
177. 7 <=> quiet(john) [avatar definition]
179. ~quiet(john) <- (~7) [avatar component clause 177]
181. 8 <=> strong(john) [avatar definition]
183. strong(john) <- (8) [avatar component clause 181]
185. 9 <=> creative(sK2) [avatar definition]
187. ~creative(sK2) <- (~9) [avatar component clause 185]
188. ~7 | 8 | ~9 [avatar split clause 175,185,181,177]
190. 10 <=> ! [X1] : creative(X1) [avatar definition]
191. creative(X1) <- (10) [avatar component clause 190]
231. quiet(X0) | ~funny(X0) | wise(X0) [subsumption resolution 121,168]
232. quiet(X0) | wise(X0) [subsumption resolution 231,172]
240. humble(X1) | creative(X1) [subsumption resolution 126,171]
241. creative(X1) [subsumption resolution 240,171]
242. 10 [avatar split clause 241,190]
255. $false <- (2) [subsumption resolution 147,168]
256. ~2 [avatar contradiction clause 255]
265. wise(john) <- (~7) [resolution 232,179]
266. $false <- (~7) [subsumption resolution 265,138]
267. 7 [avatar contradiction clause 266]
268. $false <- (~9, 10) [subsumption resolution 187,191]
269. 9 | ~10 [avatar contradiction clause 268]
270. $false <- (6, 8) [subsumption resolution 183,164]
271. ~6 | ~8 [avatar contradiction clause 270]
272. $false [avatar sat refutation 165,188,242,256,267,269,271]
% SZS output end Proof for 5098546574123742992368110
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
If susan is not curious or humble then someone is rich or quiet. Everyone who is not rich or not brave is strong. If paul is not curious then paul is either not curious or not creative and vice versa. If alice is either not patient or creative then someone is either not creative or wise and vice versa. Everyone who is both calm and humble is both not happy and not kind. Everyone who is strong or not funny is not patient and vice versa. If someone is both not generous and not tall then fred is quiet or not funny and vice versa. Everyone who is either rich or strong is either not generous or generous and vice versa. If susan is creative or generous then someone is not kind and vice versa. Everyone who is not quiet is either not kind or not happy and vice versa. Everyone who is not tall is either not funny or not rich. If alice is tall or happy then someone is either not patient or creative. Everyone who is rich or patient is both humble and creative and vice versa. If someone is either not funny or generous then john is both not rich and not generous. If someone is rich then mary is either generous or calm. Everyone who is both not brave and tall is quiet or not quiet and vice versa. Someone is not strong or funny. Paul is not rich or kind. Someone is not wise or not old. Paul is either not tall or tall. Someone is strong or not happy. Someone is either patient or not brave. | Susan is funny. | neutral | (((~curious(susan)|humble(susan)))=>(?[X]:((rich(X)|quiet(X)))))&
(![X]:((~rich(X)|~brave(X))=>strong(X)))&
((~curious(paul))<=>((~curious(paul)<~>~creative(paul))))&
(((~patient(alice)<~>creative(alice)))<=>(?[X]:((~creative(X)<~>wise(X)))))&
(![X]:((calm(X)&humble(X))=>(~happy(X)&~kind(X))))&
(![X]:((strong(X)|~funny(X))<=>~patient(X)))&
((?[X]:((~generous(X)&~tall(X))))<=>((quiet(fred)|~funny(fred))))&
(![X]:((rich(X)<~>strong(X))<=>(~generous(X)<~>generous(X))))&
(((creative(susan)|generous(susan)))<=>(?[X]:(~kind(X))))&
(![X]:(~quiet(X)<=>(~kind(X)<~>~happy(X))))&
(![X]:(~tall(X)=>(~funny(X)<~>~rich(X))))&
(((tall(alice)|happy(alice)))=>(?[X]:((~patient(X)<~>creative(X)))))&
(![X]:((rich(X)|patient(X))<=>(humble(X)&creative(X))))&
((?[X]:((~funny(X)<~>generous(X))))=>((~rich(john)&~generous(john))))&
((?[X]:(rich(X)))=>((generous(mary)<~>calm(mary))))&
(![X]:((~brave(X)&tall(X))<=>(quiet(X)|~quiet(X))))&
(?[X]:((~strong(X)|funny(X))))&
((~rich(paul)|kind(paul)))&
(?[X]:((~wise(X)|~old(X))))&
((~tall(paul)<~>tall(paul)))&
(?[X]:((strong(X)|~happy(X))))&
(?[X]:((patient(X)<~>~brave(X)))) | funny(susan) | [] | null | 0 |
Everyone who is both calm and patient is not calm or funny.
If someone is both old and not curious then someone is either not funny or not rich and vice versa.
If someone is not happy or not wise then alice is both tall and generous.
Everyone who is not wise or quiet is both not tall and not wise and vice versa.
Everyone who is both curious and brave is both curious and not creative and vice versa.
Everyone who is not generous is both not happy and not calm and vice versa.
Everyone who is patient is not brave or not old and vice versa.
Everyone who is kind is curious.
If fred is not patient or brave then susan is both not rich and rich.
If fred is both not rich and tall then someone is both quiet and not strong and vice versa.
If someone is not tall or not creative then someone is not generous and vice versa.
Everyone who is either humble or not kind is either happy or tall and vice versa.
Everyone who is both not quiet and not strong is both not kind and not patient.
If lucy is both creative and strong then john is not brave or not funny and vice versa.
Everyone who is not creative is either rich or funny and vice versa.
Someone is not funny or rich.
Fred is either not kind or funny.
Someone is not happy or funny.
Fred is both not old and not humble.
Someone is either not curious or not funny.
Someone is not humble.
Someone is not happy or creative. | Alice is not funny. | neutral | (![X]:((calm(X)&patient(X))=>(~calm(X)|funny(X))))&
((?[X]:((old(X)&~curious(X))))<=>(?[X]:((~funny(X)<~>~rich(X)))))&
((?[X]:((~happy(X)|~wise(X))))=>((tall(alice)&generous(alice))))&
(![X]:((~wise(X)|quiet(X))<=>(~tall(X)&~wise(X))))&
(![X]:((curious(X)&brave(X))<=>(curious(X)&~creative(X))))&
(![X]:(~generous(X)<=>(~happy(X)&~calm(X))))&
(![X]:(patient(X)<=>(~brave(X)|~old(X))))&
(![X]:(kind(X)=>curious(X)))&
(((~patient(fred)|brave(fred)))=>((~rich(susan)&rich(susan))))&
(((~rich(fred)&tall(fred)))<=>(?[X]:((quiet(X)&~strong(X)))))&
((?[X]:((~tall(X)|~creative(X))))<=>(?[X]:(~generous(X))))&
(![X]:((humble(X)<~>~kind(X))<=>(happy(X)<~>tall(X))))&
(![X]:((~quiet(X)&~strong(X))=>(~kind(X)&~patient(X))))&
(((creative(lucy)&strong(lucy)))<=>((~brave(john)|~funny(john))))&
(![X]:(~creative(X)<=>(rich(X)<~>funny(X))))&
(?[X]:((~funny(X)|rich(X))))&
((~kind(fred)<~>funny(fred)))&
(?[X]:((~happy(X)|funny(X))))&
((~old(fred)&~humble(fred)))&
(?[X]:((~curious(X)<~>~funny(X))))&
(?[X]:(~humble(X)))&
(?[X]:((~happy(X)|creative(X)))) | ~funny(alice) | [] | null | 0 |
If someone is curious then someone is either not generous or not patient.
If someone is either old or not wise then paul is either not creative or happy.
Everyone who is not humble is not curious or old and vice versa.
If fred is not humble or not funny then paul is both patient and not rich and vice versa.
If someone is both wise and curious then someone is rich or not happy.
If someone is either not rich or strong then someone is either not tall or not happy.
Everyone who is not curious or kind is either tall or generous and vice versa.
If fred is both brave and rich then john is not brave.
If someone is either kind or curious then someone is curious and vice versa.
Everyone who is both not tall and kind is not wise or not tall.
Everyone who is not funny is either kind or not rich and vice versa.
Everyone who is rich is not creative or not happy.
If mary is both funny and calm then someone is not curious and vice versa.
Everyone who is funny is not patient or not rich and vice versa.
If someone is not strong then someone is both wise and not calm and vice versa.
Everyone who is calm or creative is both happy and patient.
Fred is not rich.
Fred is not rich or calm.
Someone is both not strong and not humble.
Someone is both rich and calm.
Susan is not strong or kind.
Someone is happy. | Susan is not brave. | neutral | ((?[X]:(curious(X)))=>(?[X]:((~generous(X)<~>~patient(X)))))&
((?[X]:((old(X)<~>~wise(X))))=>((~creative(paul)<~>happy(paul))))&
(![X]:(~humble(X)<=>(~curious(X)|old(X))))&
(((~humble(fred)|~funny(fred)))<=>((patient(paul)&~rich(paul))))&
((?[X]:((wise(X)&curious(X))))=>(?[X]:((rich(X)|~happy(X)))))&
((?[X]:((~rich(X)<~>strong(X))))=>(?[X]:((~tall(X)<~>~happy(X)))))&
(![X]:((~curious(X)|kind(X))<=>(tall(X)<~>generous(X))))&
(((brave(fred)&rich(fred)))=>(~brave(john)))&
((?[X]:((kind(X)<~>curious(X))))<=>(?[X]:(curious(X))))&
(![X]:((~tall(X)&kind(X))=>(~wise(X)|~tall(X))))&
(![X]:(~funny(X)<=>(kind(X)<~>~rich(X))))&
(![X]:(rich(X)=>(~creative(X)|~happy(X))))&
(((funny(mary)&calm(mary)))<=>(?[X]:(~curious(X))))&
(![X]:(funny(X)<=>(~patient(X)|~rich(X))))&
((?[X]:(~strong(X)))<=>(?[X]:((wise(X)&~calm(X)))))&
(![X]:((calm(X)|creative(X))=>(happy(X)&patient(X))))&
(~rich(fred))&
((~rich(fred)|calm(fred)))&
(?[X]:((~strong(X)&~humble(X))))&
(?[X]:((rich(X)&calm(X))))&
((~strong(susan)|kind(susan)))&
(?[X]:(happy(X))) | ~brave(susan) | [] | null | 0 |
If someone is not generous or not rich then someone is either not strong or generous. Everyone who is funny is both humble and curious and vice versa. Everyone who is not calm or patient is either not tall or not strong and vice versa. Everyone who is both not strong and not tall is both humble and happy. Everyone who is not curious or not patient is humble. If lucy is quiet or not tall then someone is both rich and not kind. Everyone who is either not kind or not curious is both not happy and creative. If someone is not humble or funny then susan is both not rich and rich. Everyone who is not old or not curious is not calm. If someone is both not brave and creative then someone is kind or calm and vice versa. If someone is funny or calm then mary is both wise and not creative and vice versa. If paul is both not creative and brave then someone is both strong and not calm and vice versa. Everyone who is either not wise or generous is tall or brave. If someone is not patient then someone is either funny or not brave and vice versa. Everyone who is both not patient and wise is not wise. Everyone who is not old or calm is either not patient or wise and vice versa. Someone is not old or not wise. Susan is either not quiet or curious. Someone is either not kind or calm. Someone is either patient or wise. Someone is curious or generous. Someone is rich or tall. | Paul is not calm. | entailment | ((?[X]:((~generous(X)|~rich(X))))=>(?[X]:((~strong(X)<~>generous(X)))))&
(![X]:(funny(X)<=>(humble(X)&curious(X))))&
(![X]:((~calm(X)|patient(X))<=>(~tall(X)<~>~strong(X))))&
(![X]:((~strong(X)&~tall(X))=>(humble(X)&happy(X))))&
(![X]:((~curious(X)|~patient(X))=>humble(X)))&
(((quiet(lucy)|~tall(lucy)))=>(?[X]:((rich(X)&~kind(X)))))&
(![X]:((~kind(X)<~>~curious(X))=>(~happy(X)&creative(X))))&
((?[X]:((~humble(X)|funny(X))))=>((~rich(susan)&rich(susan))))&
(![X]:((~old(X)|~curious(X))=>~calm(X)))&
((?[X]:((~brave(X)&creative(X))))<=>(?[X]:((kind(X)|calm(X)))))&
((?[X]:((funny(X)|calm(X))))<=>((wise(mary)&~creative(mary))))&
(((~creative(paul)&brave(paul)))<=>(?[X]:((strong(X)&~calm(X)))))&
(![X]:((~wise(X)<~>generous(X))=>(tall(X)|brave(X))))&
((?[X]:(~patient(X)))<=>(?[X]:((funny(X)<~>~brave(X)))))&
(![X]:((~patient(X)&wise(X))=>~wise(X)))&
(![X]:((~old(X)|calm(X))<=>(~patient(X)<~>wise(X))))&
(?[X]:((~old(X)|~wise(X))))&
((~quiet(susan)<~>curious(susan)))&
(?[X]:((~kind(X)<~>calm(X))))&
(?[X]:((patient(X)<~>wise(X))))&
(?[X]:((curious(X)|generous(X))))&
(?[X]:((rich(X)|tall(X)))) | ~calm(paul) | [
"p1",
"p7",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 4818384640162261166490789
% SZS output start Proof for 4818384640162261166490789
2. ! [X0] : (funny(X0) <=> (curious(X0) & humble(X0))) [input p1]
8. ? [X0] : (funny(X0) | ~humble(X0)) => (rich(susan) & ~rich(susan)) [input p7]
9. ! [X0] : ((~curious(X0) | ~old(X0)) => ~calm(X0)) [input p8]
23. calm(paul) [input hypothesis]
33. (rich(susan) & ~rich(susan)) | ! [X0] : (~funny(X0) & humble(X0)) [ennf transformation 8]
34. ! [X0] : (~calm(X0) | (curious(X0) & old(X0))) [ennf transformation 9]
43. ! [X0] : ((funny(X0) | (~curious(X0) | ~humble(X0))) & ((curious(X0) & humble(X0)) | ~funny(X0))) [nnf transformation 2]
44. ! [X0] : ((funny(X0) | ~curious(X0) | ~humble(X0)) & ((curious(X0) & humble(X0)) | ~funny(X0))) [flattening 43]
92. ~curious(X0) | funny(X0) | ~humble(X0) [cnf transformation 44]
111. ~rich(susan) | humble(X0) [cnf transformation 33]
112. ~rich(susan) | ~funny(X0) [cnf transformation 33]
113. rich(susan) | humble(X0) [cnf transformation 33]
114. rich(susan) | ~funny(X0) [cnf transformation 33]
116. ~calm(X0) | curious(X0) [cnf transformation 34]
153. calm(paul) [cnf transformation 23]
194. 9 <=> ! [X0] : ~funny(X0) [avatar definition]
195. ~funny(X0) <- (9) [avatar component clause 194]
197. 10 <=> rich(susan) [avatar definition]
200. 9 | 10 [avatar split clause 114,197,194]
202. 11 <=> ! [X0] : humble(X0) [avatar definition]
203. humble(X0) <- (11) [avatar component clause 202]
204. 11 | 10 [avatar split clause 113,197,202]
205. 9 | ~10 [avatar split clause 112,197,194]
206. 11 | ~10 [avatar split clause 111,197,202]
365. curious(paul) [resolution 116,153]
372. funny(paul) | ~humble(paul) [resolution 92,365]
375. ~humble(paul) <- (9) [subsumption resolution 372,195]
376. $false <- (9, 11) [subsumption resolution 375,203]
377. ~9 | ~11 [avatar contradiction clause 376]
384. $false [avatar sat refutation 200,204,205,206,377]
% SZS output end Proof for 4818384640162261166490789
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
If alice is funny then someone is old.
If mary is both rich and not calm then someone is not tall and vice versa.
Everyone who is curious is quiet or not strong and vice versa.
Everyone who is either tall or not humble is either brave or quiet.
If someone is tall then fred is humble.
If fred is calm or strong then someone is wise or not strong and vice versa.
Everyone who is both curious and rich is either not calm or rich.
If someone is both not humble and quiet then mary is either not tall or patient.
If someone is either not humble or not happy then someone is either curious or humble and vice versa.
If susan is not generous or not humble then someone is either not generous or kind.
If paul is either brave or not happy then someone is both generous and not tall.
If someone is not kind or not brave then susan is both not old and quiet and vice versa.
If john is both patient and funny then someone is either not funny or rich and vice versa.
If someone is either not wise or not quiet then someone is either not wise or not curious and vice versa.
Everyone who is either not patient or not brave is both old and not brave.
If susan is quiet or not old then lucy is either strong or curious and vice versa.
Mary is both happy and not strong.
Paul is not happy.
Mary is not generous or not funny.
Someone is patient.
Paul is either not wise or creative.
Someone is not patient.
Someone is not patient or quiet. | Paul is not patient. | contradiction | ((funny(alice))=>(?[X]:(old(X))))&
(((rich(mary)&~calm(mary)))<=>(?[X]:(~tall(X))))&
(![X]:(curious(X)<=>(quiet(X)|~strong(X))))&
(![X]:((tall(X)<~>~humble(X))=>(brave(X)<~>quiet(X))))&
((?[X]:(tall(X)))=>(humble(fred)))&
(((calm(fred)|strong(fred)))<=>(?[X]:((wise(X)|~strong(X)))))&
(![X]:((curious(X)&rich(X))=>(~calm(X)<~>rich(X))))&
((?[X]:((~humble(X)&quiet(X))))=>((~tall(mary)<~>patient(mary))))&
((?[X]:((~humble(X)<~>~happy(X))))<=>(?[X]:((curious(X)<~>humble(X)))))&
(((~generous(susan)|~humble(susan)))=>(?[X]:((~generous(X)<~>kind(X)))))&
(((brave(paul)<~>~happy(paul)))=>(?[X]:((generous(X)&~tall(X)))))&
((?[X]:((~kind(X)|~brave(X))))<=>((~old(susan)&quiet(susan))))&
(((patient(john)&funny(john)))<=>(?[X]:((~funny(X)<~>rich(X)))))&
((?[X]:((~wise(X)<~>~quiet(X))))<=>(?[X]:((~wise(X)<~>~curious(X)))))&
(![X]:((~patient(X)<~>~brave(X))=>(old(X)&~brave(X))))&
(((quiet(susan)|~old(susan)))<=>((strong(lucy)<~>curious(lucy))))&
((happy(mary)&~strong(mary)))&
(~happy(paul))&
((~generous(mary)|~funny(mary)))&
(?[X]:(patient(X)))&
((~wise(paul)<~>creative(paul)))&
(?[X]:(~patient(X)))&
(?[X]:((~patient(X)|quiet(X)))) | ~patient(paul) | [
"p1",
"p2",
"p6",
"p10",
"p14",
"p16",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 7953246412311923243752966
% SZS output start Proof for 7953246412311923243752966
2. (~calm(mary) & rich(mary)) <=> ? [X0] : ~tall(X0) [input p1]
3. ! [X0] : (curious(X0) <=> (~strong(X0) | quiet(X0))) [input p2]
7. ! [X0] : ((rich(X0) & curious(X0)) => (~calm(X0) <~> rich(X0))) [input p6]
11. (brave(paul) <~> ~happy(paul)) => ? [X0] : (~tall(X0) & generous(X0)) [input p10]
15. ! [X0] : ((~patient(X0) <~> ~brave(X0)) => (~brave(X0) & old(X0))) [input p14]
17. ~strong(mary) & happy(mary) [input p16]
18. ~happy(paul) [input p17]
24. ~patient(paul) [input hypothesis]
30. ! [X0] : ((~calm(X0) <~> rich(X0)) | (~rich(X0) | ~curious(X0))) [ennf transformation 7]
31. ! [X0] : ((~calm(X0) <~> rich(X0)) | ~rich(X0) | ~curious(X0)) [flattening 30]
34. ? [X0] : (~tall(X0) & generous(X0)) | (brave(paul) <=> ~happy(paul)) [ennf transformation 11]
35. ! [X0] : ((~brave(X0) & old(X0)) | (~patient(X0) <=> ~brave(X0))) [ennf transformation 15]
38. ((~calm(mary) & rich(mary)) | ! [X0] : tall(X0)) & (? [X0] : ~tall(X0) | (calm(mary) | ~rich(mary))) [nnf transformation 2]
39. ((~calm(mary) & rich(mary)) | ! [X0] : tall(X0)) & (? [X0] : ~tall(X0) | calm(mary) | ~rich(mary)) [flattening 38]
40. ((~calm(mary) & rich(mary)) | ! [X0] : tall(X0)) & (? [X1] : ~tall(X1) | calm(mary) | ~rich(mary)) [rectify 39]
41. ? [X1] : ~tall(X1) => ~tall(sK1) [choice axiom]
42. ((~calm(mary) & rich(mary)) | ! [X0] : tall(X0)) & (~tall(sK1) | calm(mary) | ~rich(mary)) [skolemisation 40,41]
43. ! [X0] : ((curious(X0) | (strong(X0) & ~quiet(X0))) & ((~strong(X0) | quiet(X0)) | ~curious(X0))) [nnf transformation 3]
44. ! [X0] : ((curious(X0) | (strong(X0) & ~quiet(X0))) & (~strong(X0) | quiet(X0) | ~curious(X0))) [flattening 43]
51. ! [X0] : (((~rich(X0) | calm(X0)) & (rich(X0) | ~calm(X0))) | ~rich(X0) | ~curious(X0)) [nnf transformation 31]
61. ? [X0] : (~tall(X0) & generous(X0)) | ((brave(paul) | happy(paul)) & (~happy(paul) | ~brave(paul))) [nnf transformation 34]
62. ? [X0] : (~tall(X0) & generous(X0)) => (~tall(sK6) & generous(sK6)) [choice axiom]
63. (~tall(sK6) & generous(sK6)) | ((brave(paul) | happy(paul)) & (~happy(paul) | ~brave(paul))) [skolemisation 61,62]
79. ! [X0] : ((~brave(X0) & old(X0)) | ((~patient(X0) | brave(X0)) & (~brave(X0) | patient(X0)))) [nnf transformation 35]
91. rich(mary) | tall(X0) [cnf transformation 42]
92. ~calm(mary) | tall(X0) [cnf transformation 42]
95. strong(X0) | curious(X0) [cnf transformation 44]
106. ~rich(X0) | calm(X0) | ~rich(X0) | ~curious(X0) [cnf transformation 51]
124. ~tall(sK6) | brave(paul) | happy(paul) [cnf transformation 63]
146. ~brave(X0) | ~brave(X0) | patient(X0) [cnf transformation 79]
155. ~strong(mary) [cnf transformation 17]
156. ~happy(paul) [cnf transformation 18]
163. ~patient(paul) [cnf transformation 24]
164. ~brave(X0) | patient(X0) [duplicate literal removal 146]
165. ~curious(X0) | calm(X0) | ~rich(X0) [duplicate literal removal 106]
176. 3 <=> ! [X0] : tall(X0) [avatar definition]
177. tall(X0) <- (3) [avatar component clause 176]
179. 4 <=> calm(mary) [avatar definition]
182. 3 | ~4 [avatar split clause 92,179,176]
184. 5 <=> rich(mary) [avatar definition]
186. rich(mary) <- (5) [avatar component clause 184]
187. 3 | 5 [avatar split clause 91,184,176]
297. 30 <=> happy(paul) [avatar definition]
301. 31 <=> brave(paul) [avatar definition]
303. brave(paul) <- (31) [avatar component clause 301]
305. 32 <=> tall(sK6) [avatar definition]
307. ~tall(sK6) <- (~32) [avatar component clause 305]
308. 30 | 31 | ~32 [avatar split clause 124,305,301,297]
421. ~30 [avatar split clause 156,297]
453. curious(mary) [resolution 95,155]
457. patient(paul) <- (31) [resolution 164,303]
458. $false <- (31) [subsumption resolution 457,163]
459. ~31 [avatar contradiction clause 458]
475. calm(mary) | ~rich(mary) [resolution 165,453]
509. calm(mary) <- (5) [subsumption resolution 475,186]
510. 4 | ~5 [avatar split clause 509,184,179]
515. $false <- (3, ~32) [resolution 307,177]
516. ~3 | 32 [avatar contradiction clause 515]
517. $false [avatar sat refutation 182,187,308,421,459,510,516]
% SZS output end Proof for 7953246412311923243752966
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not quiet or not curious is not kind.
If mary is either rich or not curious then mary is both quiet and not tall and vice versa.
Everyone who is not old or strong is not creative or not patient.
Everyone who is not humble is both not rich and rich.
Everyone who is not happy or curious is not kind or not curious and vice versa.
If alice is humble or happy then alice is both kind and humble.
If someone is both strong and not curious then susan is calm and vice versa.
Everyone who is either not quiet or not humble is not creative.
If fred is not rich or generous then fred is humble or kind.
If lucy is brave or not old then lucy is either kind or not humble and vice versa.
Everyone who is both humble and wise is either not calm or rich.
If fred is not funny then mary is either tall or not happy.
Everyone who is patient or brave is either not rich or not calm.
If someone is both not rich and old then someone is either funny or not rich and vice versa.
If susan is funny then alice is not happy and vice versa.
Everyone who is rich or not quiet is not happy.
Someone is both not happy and not curious.
Someone is not tall or tall.
Paul is not quiet.
Someone is quiet.
Someone is not brave.
Alice is not quiet or not patient.
Mary is happy.
Someone is both not brave and quiet. | Paul is creative. | contradiction | (![X]:((~quiet(X)<~>~curious(X))=>~kind(X)))&
(((rich(mary)<~>~curious(mary)))<=>((quiet(mary)&~tall(mary))))&
(![X]:((~old(X)|strong(X))=>(~creative(X)|~patient(X))))&
(![X]:(~humble(X)=>(~rich(X)&rich(X))))&
(![X]:((~happy(X)|curious(X))<=>(~kind(X)|~curious(X))))&
(((humble(alice)|happy(alice)))=>((kind(alice)&humble(alice))))&
((?[X]:((strong(X)&~curious(X))))<=>(calm(susan)))&
(![X]:((~quiet(X)<~>~humble(X))=>~creative(X)))&
(((~rich(fred)|generous(fred)))=>((humble(fred)|kind(fred))))&
(((brave(lucy)|~old(lucy)))<=>((kind(lucy)<~>~humble(lucy))))&
(![X]:((humble(X)&wise(X))=>(~calm(X)<~>rich(X))))&
((~funny(fred))=>((tall(mary)<~>~happy(mary))))&
(![X]:((patient(X)|brave(X))=>(~rich(X)<~>~calm(X))))&
((?[X]:((~rich(X)&old(X))))<=>(?[X]:((funny(X)<~>~rich(X)))))&
((funny(susan))<=>(~happy(alice)))&
(![X]:((rich(X)|~quiet(X))=>~happy(X)))&
(?[X]:((~happy(X)&~curious(X))))&
(?[X]:((~tall(X)|tall(X))))&
(~quiet(paul))&
(?[X]:(quiet(X)))&
(?[X]:(~brave(X)))&
((~quiet(alice)|~patient(alice)))&
(happy(mary))&
(?[X]:((~brave(X)&quiet(X)))) | creative(paul) | [
"p3",
"p7",
"p18",
"hypothesis"
] | % SZS status Unsatisfiable for 8784686405187579513833361
% SZS output start Proof for 8784686405187579513833361
4. ! [X0] : (~humble(X0) => (rich(X0) & ~rich(X0))) [input p3]
8. ! [X0] : ((~quiet(X0) <~> ~humble(X0)) => ~creative(X0)) [input p7]
19. ~quiet(paul) [input p18]
25. creative(paul) [input hypothesis]
33. ! [X0] : ((rich(X0) & ~rich(X0)) | humble(X0)) [ennf transformation 4]
35. ! [X0] : (~creative(X0) | (~quiet(X0) <=> ~humble(X0))) [ennf transformation 8]
50. ! [X0] : (~creative(X0) | ((~quiet(X0) | humble(X0)) & (~humble(X0) | quiet(X0)))) [nnf transformation 35]
79. ~rich(X0) | humble(X0) [cnf transformation 33]
80. humble(X0) | rich(X0) [cnf transformation 33]
92. ~creative(X0) | ~humble(X0) | quiet(X0) [cnf transformation 50]
118. ~quiet(paul) [cnf transformation 19]
124. creative(paul) [cnf transformation 25]
149. humble(X0) [subsumption resolution 79,80]
179. ~creative(X0) | quiet(X0) [subsumption resolution 92,149]
260. quiet(paul) [resolution 179,124]
261. $false [subsumption resolution 260,118]
% SZS output end Proof for 8784686405187579513833361
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both generous and not calm then lucy is not rich and vice versa.
Everyone who is not strong or happy is either calm or not strong.
Everyone who is generous is either quiet or not generous and vice versa.
Everyone who is both creative and not tall is either not funny or not strong.
Everyone who is either wise or patient is patient and vice versa.
Everyone who is happy or not quiet is both generous and not old and vice versa.
If susan is both wise and rich then lucy is either tall or not brave and vice versa.
If someone is generous or wise then someone is not calm and vice versa.
Everyone who is either strong or not kind is both not curious and strong.
If fred is either patient or not wise then susan is either not curious or tall.
If paul is strong or not rich then someone is not patient.
Everyone who is either not calm or quiet is both curious and kind and vice versa.
Everyone who is not quiet is kind and vice versa.
Everyone who is both rich and creative is both curious and not old and vice versa.
If susan is not quiet or calm then someone is both old and tall and vice versa.
Someone is either happy or not brave.
Someone is quiet.
Lucy is not funny or tall.
Someone is wise or not funny.
Susan is not humble.
Susan is kind or not humble. | Susan is strong. | entailment | ((?[X]:((generous(X)&~calm(X))))<=>(~rich(lucy)))&
(![X]:((~strong(X)|happy(X))=>(calm(X)<~>~strong(X))))&
(![X]:(generous(X)<=>(quiet(X)<~>~generous(X))))&
(![X]:((creative(X)&~tall(X))=>(~funny(X)<~>~strong(X))))&
(![X]:((wise(X)<~>patient(X))<=>patient(X)))&
(![X]:((happy(X)|~quiet(X))<=>(generous(X)&~old(X))))&
(((wise(susan)&rich(susan)))<=>((tall(lucy)<~>~brave(lucy))))&
((?[X]:((generous(X)|wise(X))))<=>(?[X]:(~calm(X))))&
(![X]:((strong(X)<~>~kind(X))=>(~curious(X)&strong(X))))&
(((patient(fred)<~>~wise(fred)))=>((~curious(susan)<~>tall(susan))))&
(((strong(paul)|~rich(paul)))=>(?[X]:(~patient(X))))&
(![X]:((~calm(X)<~>quiet(X))<=>(curious(X)&kind(X))))&
(![X]:(~quiet(X)<=>kind(X)))&
(![X]:((rich(X)&creative(X))<=>(curious(X)&~old(X))))&
(((~quiet(susan)|calm(susan)))<=>(?[X]:((old(X)&tall(X)))))&
(?[X]:((happy(X)<~>~brave(X))))&
(?[X]:(quiet(X)))&
((~funny(lucy)|tall(lucy)))&
(?[X]:((wise(X)|~funny(X))))&
(~humble(susan))&
((kind(susan)|~humble(susan))) | strong(susan) | [
"p2",
"p8",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 6330202970837941617505296
% SZS output start Proof for 6330202970837941617505296
3. ! [X0] : (generous(X0) <=> (quiet(X0) <~> ~generous(X0))) [input p2]
9. ! [X0] : ((strong(X0) <~> ~kind(X0)) => (strong(X0) & ~curious(X0))) [input p8]
13. ! [X0] : (~quiet(X0) <=> kind(X0)) [input p12]
22. ~strong(susan) [input hypothesis]
29. ! [X0] : ((strong(X0) & ~curious(X0)) | (strong(X0) <=> ~kind(X0))) [ennf transformation 9]
37. ! [X0] : ((generous(X0) | ((quiet(X0) | generous(X0)) & (~generous(X0) | ~quiet(X0)))) & (((generous(X0) | ~quiet(X0)) & (~generous(X0) | quiet(X0))) | ~generous(X0))) [nnf transformation 3]
49. ! [X0] : ((strong(X0) & ~curious(X0)) | ((strong(X0) | kind(X0)) & (~kind(X0) | ~strong(X0)))) [nnf transformation 29]
55. ! [X0] : ((~quiet(X0) | ~kind(X0)) & (kind(X0) | quiet(X0))) [nnf transformation 13]
77. ~generous(X0) | quiet(X0) | ~generous(X0) [cnf transformation 37]
80. generous(X0) | quiet(X0) | generous(X0) [cnf transformation 37]
104. strong(X0) | strong(X0) | kind(X0) [cnf transformation 49]
118. ~quiet(X0) | ~kind(X0) [cnf transformation 55]
133. ~strong(susan) [cnf transformation 22]
134. kind(X0) | strong(X0) [duplicate literal removal 104]
137. ~generous(X0) | quiet(X0) [duplicate literal removal 77]
138. generous(X0) | quiet(X0) [duplicate literal removal 80]
158. quiet(X0) [subsumption resolution 137,138]
229. ~kind(X0) [subsumption resolution 118,158]
267. strong(X0) [resolution 134,229]
268. $false [resolution 267,133]
% SZS output end Proof for 6330202970837941617505296
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is old is either not happy or not kind and vice versa.
Everyone who is curious is both not strong and humble.
Everyone who is not brave is humble and vice versa.
Everyone who is both not kind and not happy is both not curious and not patient and vice versa.
Everyone who is not creative or rich is not old and vice versa.
Everyone who is not kind or tall is both calm and not curious and vice versa.
Everyone who is not rich is not happy or rich and vice versa.
Everyone who is both not tall and humble is both not old and quiet and vice versa.
If someone is either not wise or creative then someone is both not funny and not kind.
Everyone who is not creative is both calm and not wise.
Everyone who is both generous and not wise is either not kind or not rich.
If someone is calm or not funny then john is both not rich and wise.
Everyone who is both creative and humble is not kind or quiet and vice versa.
Everyone who is kind or not quiet is tall or not humble.
Everyone who is either wise or old is not quiet.
If someone is tall then lucy is both brave and not patient and vice versa.
Paul is both not wise and patient.
Someone is not humble.
Someone is either generous or not happy.
Fred is either rich or funny.
Someone is quiet or not happy.
Susan is not strong or wise. | Paul is not happy. | entailment | (![X]:(old(X)<=>(~happy(X)<~>~kind(X))))&
(![X]:(curious(X)=>(~strong(X)&humble(X))))&
(![X]:(~brave(X)<=>humble(X)))&
(![X]:((~kind(X)&~happy(X))<=>(~curious(X)&~patient(X))))&
(![X]:((~creative(X)|rich(X))<=>~old(X)))&
(![X]:((~kind(X)|tall(X))<=>(calm(X)&~curious(X))))&
(![X]:(~rich(X)<=>(~happy(X)|rich(X))))&
(![X]:((~tall(X)&humble(X))<=>(~old(X)&quiet(X))))&
((?[X]:((~wise(X)<~>creative(X))))=>(?[X]:((~funny(X)&~kind(X)))))&
(![X]:(~creative(X)=>(calm(X)&~wise(X))))&
(![X]:((generous(X)&~wise(X))=>(~kind(X)<~>~rich(X))))&
((?[X]:((calm(X)|~funny(X))))=>((~rich(john)&wise(john))))&
(![X]:((creative(X)&humble(X))<=>(~kind(X)|quiet(X))))&
(![X]:((kind(X)|~quiet(X))=>(tall(X)|~humble(X))))&
(![X]:((wise(X)<~>old(X))=>~quiet(X)))&
((?[X]:(tall(X)))<=>((brave(lucy)&~patient(lucy))))&
((~wise(paul)&patient(paul)))&
(?[X]:(~humble(X)))&
(?[X]:((generous(X)<~>~happy(X))))&
((rich(fred)<~>funny(fred)))&
(?[X]:((quiet(X)|~happy(X))))&
((~strong(susan)|wise(susan))) | ~happy(paul) | [
"p6",
"hypothesis"
] | % SZS status Unsatisfiable for 4846692718912551483784484
% SZS output start Proof for 4846692718912551483784484
7. ! [X0] : (~rich(X0) <=> (rich(X0) | ~happy(X0))) [input p6]
23. happy(paul) [input hypothesis]
44. ! [X0] : ((~rich(X0) | (~rich(X0) & happy(X0))) & ((rich(X0) | ~happy(X0)) | rich(X0))) [nnf transformation 7]
45. ! [X0] : ((~rich(X0) | (~rich(X0) & happy(X0))) & (rich(X0) | ~happy(X0) | rich(X0))) [flattening 44]
88. rich(X0) | ~happy(X0) | rich(X0) [cnf transformation 45]
90. ~rich(X0) | ~rich(X0) [cnf transformation 45]
127. happy(paul) [cnf transformation 23]
128. rich(X0) | ~happy(X0) [duplicate literal removal 88]
129. ~rich(X0) [duplicate literal removal 90]
130. ~happy(X0) [subsumption resolution 128,129]
182. $false [subsumption resolution 127,130]
% SZS output end Proof for 4846692718912551483784484
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either wise or generous is quiet or strong and vice versa.
Everyone who is either not patient or old is both not kind and not old and vice versa.
If someone is both not humble and not tall then alice is kind.
Everyone who is both not rich and humble is not old.
Everyone who is not curious or not old is funny.
Everyone who is not happy or not tall is not happy or patient and vice versa.
Everyone who is not kind or not curious is not generous or not calm.
If someone is both kind and funny then mary is tall and vice versa.
Everyone who is patient is humble and vice versa.
If someone is not old then someone is not happy and vice versa.
Everyone who is either not quiet or patient is both creative and kind.
Everyone who is generous is not brave or curious.
Everyone who is both funny and curious is not funny and vice versa.
Everyone who is both not quiet and not funny is not funny or calm and vice versa.
Everyone who is both quiet and rich is either generous or not patient and vice versa.
Everyone who is both not brave and not patient is either calm or not humble and vice versa.
John is curious or tall.
Someone is either curious or not old.
Someone is curious or rich.
Paul is either curious or patient.
Fred is quiet.
Someone is either strong or not wise.
Alice is either calm or kind. | Fred is not wise. | neutral | (![X]:((wise(X)<~>generous(X))<=>(quiet(X)|strong(X))))&
(![X]:((~patient(X)<~>old(X))<=>(~kind(X)&~old(X))))&
((?[X]:((~humble(X)&~tall(X))))=>(kind(alice)))&
(![X]:((~rich(X)&humble(X))=>~old(X)))&
(![X]:((~curious(X)|~old(X))=>funny(X)))&
(![X]:((~happy(X)|~tall(X))<=>(~happy(X)|patient(X))))&
(![X]:((~kind(X)|~curious(X))=>(~generous(X)|~calm(X))))&
((?[X]:((kind(X)&funny(X))))<=>(tall(mary)))&
(![X]:(patient(X)<=>humble(X)))&
((?[X]:(~old(X)))<=>(?[X]:(~happy(X))))&
(![X]:((~quiet(X)<~>patient(X))=>(creative(X)&kind(X))))&
(![X]:(generous(X)=>(~brave(X)|curious(X))))&
(![X]:((funny(X)&curious(X))<=>~funny(X)))&
(![X]:((~quiet(X)&~funny(X))<=>(~funny(X)|calm(X))))&
(![X]:((quiet(X)&rich(X))<=>(generous(X)<~>~patient(X))))&
(![X]:((~brave(X)&~patient(X))<=>(calm(X)<~>~humble(X))))&
((curious(john)|tall(john)))&
(?[X]:((curious(X)<~>~old(X))))&
(?[X]:((curious(X)|rich(X))))&
((curious(paul)<~>patient(paul)))&
(quiet(fred))&
(?[X]:((strong(X)<~>~wise(X))))&
((calm(alice)<~>kind(alice))) | ~wise(fred) | [] | null | 0 |
If fred is not curious then someone is creative or old and vice versa.
If someone is brave then john is kind or brave.
Everyone who is both not old and old is not quiet and vice versa.
Everyone who is both not happy and generous is both not humble and creative and vice versa.
Everyone who is generous is funny or humble.
If someone is not rich then someone is not wise or not patient and vice versa.
If mary is either not happy or not funny then someone is both patient and not wise and vice versa.
Everyone who is funny or generous is both curious and calm and vice versa.
If lucy is either not strong or not curious then fred is happy.
Everyone who is not rich or not happy is tall or creative.
If alice is both old and patient then susan is either kind or calm and vice versa.
Everyone who is both not kind and not happy is not curious or tall.
Everyone who is both curious and not funny is either wise or not strong and vice versa.
Everyone who is either quiet or calm is quiet and vice versa.
Everyone who is either generous or brave is either patient or not kind and vice versa.
Everyone who is either not quiet or not strong is either curious or tall and vice versa.
Susan is not strong.
Susan is both not rich and brave.
Fred is generous or not strong.
Paul is rich or kind.
Someone is not tall.
Paul is humble or strong. | Lucy is not wise. | neutral | ((~curious(fred))<=>(?[X]:((creative(X)|old(X)))))&
((?[X]:(brave(X)))=>((kind(john)|brave(john))))&
(![X]:((~old(X)&old(X))<=>~quiet(X)))&
(![X]:((~happy(X)&generous(X))<=>(~humble(X)&creative(X))))&
(![X]:(generous(X)=>(funny(X)|humble(X))))&
((?[X]:(~rich(X)))<=>(?[X]:((~wise(X)|~patient(X)))))&
(((~happy(mary)<~>~funny(mary)))<=>(?[X]:((patient(X)&~wise(X)))))&
(![X]:((funny(X)|generous(X))<=>(curious(X)&calm(X))))&
(((~strong(lucy)<~>~curious(lucy)))=>(happy(fred)))&
(![X]:((~rich(X)|~happy(X))=>(tall(X)|creative(X))))&
(((old(alice)&patient(alice)))<=>((kind(susan)<~>calm(susan))))&
(![X]:((~kind(X)&~happy(X))=>(~curious(X)|tall(X))))&
(![X]:((curious(X)&~funny(X))<=>(wise(X)<~>~strong(X))))&
(![X]:((quiet(X)<~>calm(X))<=>quiet(X)))&
(![X]:((generous(X)<~>brave(X))<=>(patient(X)<~>~kind(X))))&
(![X]:((~quiet(X)<~>~strong(X))<=>(curious(X)<~>tall(X))))&
(~strong(susan))&
((~rich(susan)&brave(susan)))&
((generous(fred)|~strong(fred)))&
((rich(paul)|kind(paul)))&
(?[X]:(~tall(X)))&
((humble(paul)|strong(paul))) | ~wise(lucy) | [] | null | 0 |
Everyone who is either not patient or brave is both not rich and rich.
Everyone who is both not curious and happy is either old or funny.
Everyone who is either not rich or not strong is not curious or wise and vice versa.
Everyone who is not strong or curious is wise.
Everyone who is not generous or not brave is both not quiet and not patient.
If mary is not funny or not creative then mary is not funny or calm.
If someone is either not humble or patient then someone is brave or not tall and vice versa.
If susan is not rich then susan is not calm and vice versa.
If someone is funny or tall then mary is both not creative and quiet.
If susan is not tall or not rich then lucy is not old.
Everyone who is brave or creative is brave.
Everyone who is both not wise and not old is not funny and vice versa.
Everyone who is both not patient and creative is not curious or not kind and vice versa.
If someone is not curious or not old then someone is either not happy or not old and vice versa.
If someone is either calm or humble then someone is either old or not tall.
Everyone who is not strong or happy is not calm and vice versa.
John is either humble or not brave.
Someone is not old or not calm.
Mary is patient or funny.
Alice is quiet or patient.
Fred is both generous and not curious. | Susan is not patient. | entailment | (![X]:((~patient(X)<~>brave(X))=>(~rich(X)&rich(X))))&
(![X]:((~curious(X)&happy(X))=>(old(X)<~>funny(X))))&
(![X]:((~rich(X)<~>~strong(X))<=>(~curious(X)|wise(X))))&
(![X]:((~strong(X)|curious(X))=>wise(X)))&
(![X]:((~generous(X)|~brave(X))=>(~quiet(X)&~patient(X))))&
(((~funny(mary)|~creative(mary)))=>((~funny(mary)|calm(mary))))&
((?[X]:((~humble(X)<~>patient(X))))<=>(?[X]:((brave(X)|~tall(X)))))&
((~rich(susan))<=>(~calm(susan)))&
((?[X]:((funny(X)|tall(X))))=>((~creative(mary)&quiet(mary))))&
(((~tall(susan)|~rich(susan)))=>(~old(lucy)))&
(![X]:((brave(X)|creative(X))=>brave(X)))&
(![X]:((~wise(X)&~old(X))<=>~funny(X)))&
(![X]:((~patient(X)&creative(X))<=>(~curious(X)|~kind(X))))&
((?[X]:((~curious(X)|~old(X))))<=>(?[X]:((~happy(X)<~>~old(X)))))&
((?[X]:((calm(X)<~>humble(X))))=>(?[X]:((old(X)<~>~tall(X)))))&
(![X]:((~strong(X)|happy(X))<=>~calm(X)))&
((humble(john)<~>~brave(john)))&
(?[X]:((~old(X)|~calm(X))))&
((patient(mary)|funny(mary)))&
((quiet(alice)|patient(alice)))&
((generous(fred)&~curious(fred))) | ~patient(susan) | [
"p0",
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 4148175917411111708684089
% SZS output start Proof for 4148175917411111708684089
1. ! [X0] : ((~patient(X0) <~> brave(X0)) => (rich(X0) & ~rich(X0))) [input p0]
5. ! [X0] : ((~brave(X0) | ~generous(X0)) => (~patient(X0) & ~quiet(X0))) [input p4]
22. patient(susan) [input hypothesis]
27. ! [X0] : (~brave(X0) => (~patient(X0) & ~quiet(X0))) [pure predicate removal 5]
28. ! [X0] : ((rich(X0) & ~rich(X0)) | (~patient(X0) <=> brave(X0))) [ennf transformation 1]
32. ! [X0] : ((~patient(X0) & ~quiet(X0)) | brave(X0)) [ennf transformation 27]
39. ! [X0] : ((rich(X0) & ~rich(X0)) | ((~patient(X0) | ~brave(X0)) & (brave(X0) | patient(X0)))) [nnf transformation 28]
67. ~rich(X0) | brave(X0) | patient(X0) [cnf transformation 39]
68. ~rich(X0) | ~patient(X0) | ~brave(X0) [cnf transformation 39]
69. rich(X0) | brave(X0) | patient(X0) [cnf transformation 39]
70. rich(X0) | ~patient(X0) | ~brave(X0) [cnf transformation 39]
82. ~patient(X0) | brave(X0) [cnf transformation 32]
128. patient(susan) [cnf transformation 22]
129. ~brave(X0) | ~patient(X0) [subsumption resolution 68,70]
130. brave(X0) | patient(X0) [subsumption resolution 67,69]
131. brave(X0) [subsumption resolution 82,130]
280. ~patient(X0) [resolution 129,131]
281. $false [resolution 280,128]
% SZS output end Proof for 4148175917411111708684089
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is calm or kind is strong. Everyone who is generous or calm is both not creative and kind and vice versa. Everyone who is both not curious and curious is not calm. If someone is humble then paul is either not tall or generous and vice versa. If someone is both not kind and strong then paul is both not old and rich and vice versa. Everyone who is both patient and brave is tall or funny and vice versa. Everyone who is not quiet or not rich is both kind and not rich. If someone is brave then mary is tall and vice versa. Everyone who is either not patient or not calm is either not funny or not quiet. Everyone who is not tall is either patient or not curious. Everyone who is calm or funny is old and vice versa. If mary is quiet or calm then john is curious and vice versa. Everyone who is not funny or quiet is either creative or not calm. If fred is not brave or not wise then someone is either not curious or not patient and vice versa. Everyone who is both curious and not curious is either not kind or not wise and vice versa. If someone is kind then someone is humble and vice versa. Someone is not brave or not generous. Someone is kind or not rich. Paul is not patient. Someone is either strong or not patient. Someone is rich. Someone is either wise or old. Someone is creative or calm. Lucy is both tall and funny. | Paul is not humble. | neutral | (![X]:((calm(X)|kind(X))=>strong(X)))&
(![X]:((generous(X)|calm(X))<=>(~creative(X)&kind(X))))&
(![X]:((~curious(X)&curious(X))=>~calm(X)))&
((?[X]:(humble(X)))<=>((~tall(paul)<~>generous(paul))))&
((?[X]:((~kind(X)&strong(X))))<=>((~old(paul)&rich(paul))))&
(![X]:((patient(X)&brave(X))<=>(tall(X)|funny(X))))&
(![X]:((~quiet(X)|~rich(X))=>(kind(X)&~rich(X))))&
((?[X]:(brave(X)))<=>(tall(mary)))&
(![X]:((~patient(X)<~>~calm(X))=>(~funny(X)<~>~quiet(X))))&
(![X]:(~tall(X)=>(patient(X)<~>~curious(X))))&
(![X]:((calm(X)|funny(X))<=>old(X)))&
(((quiet(mary)|calm(mary)))<=>(curious(john)))&
(![X]:((~funny(X)|quiet(X))=>(creative(X)<~>~calm(X))))&
(((~brave(fred)|~wise(fred)))<=>(?[X]:((~curious(X)<~>~patient(X)))))&
(![X]:((curious(X)&~curious(X))<=>(~kind(X)<~>~wise(X))))&
((?[X]:(kind(X)))<=>(?[X]:(humble(X))))&
(?[X]:((~brave(X)|~generous(X))))&
(?[X]:((kind(X)|~rich(X))))&
(~patient(paul))&
(?[X]:((strong(X)<~>~patient(X))))&
(?[X]:(rich(X)))&
(?[X]:((wise(X)<~>old(X))))&
(?[X]:((creative(X)|calm(X))))&
((tall(lucy)&funny(lucy))) | ~humble(paul) | [] | null | 0 |
If someone is both not patient and not funny then susan is kind or curious and vice versa. If someone is both rich and not brave then someone is not brave. Everyone who is both humble and not brave is not rich or funny. Everyone who is not wise or patient is either quiet or not tall. Everyone who is both curious and not funny is both wise and brave. Everyone who is both not rich and not strong is patient or strong and vice versa. If fred is not humble then someone is not patient or not creative and vice versa. Everyone who is not generous or not kind is either humble or not rich and vice versa. Everyone who is both old and not tall is not wise or curious and vice versa. If fred is not rich then susan is both not brave and generous. If fred is not creative or not funny then someone is either not patient or humble and vice versa. Everyone who is creative or rich is either curious or calm. Everyone who is either patient or not patient is not calm or not rich and vice versa. Everyone who is either calm or quiet is not creative and vice versa. If someone is not kind then someone is either not humble or not tall. If someone is both wise and not creative then fred is patient or strong. Someone is humble or generous. Susan is tall or not creative. Alice is both creative and not wise. Someone is both not kind and not humble. Someone is both not tall and not patient. Someone is both not tall and not old. John is either not brave or not rich. Someone is both tall and not strong. | Susan is not brave. | entailment | ((?[X]:((~patient(X)&~funny(X))))<=>((kind(susan)|curious(susan))))&
((?[X]:((rich(X)&~brave(X))))=>(?[X]:(~brave(X))))&
(![X]:((humble(X)&~brave(X))=>(~rich(X)|funny(X))))&
(![X]:((~wise(X)|patient(X))=>(quiet(X)<~>~tall(X))))&
(![X]:((curious(X)&~funny(X))=>(wise(X)&brave(X))))&
(![X]:((~rich(X)&~strong(X))<=>(patient(X)|strong(X))))&
((~humble(fred))<=>(?[X]:((~patient(X)|~creative(X)))))&
(![X]:((~generous(X)|~kind(X))<=>(humble(X)<~>~rich(X))))&
(![X]:((old(X)&~tall(X))<=>(~wise(X)|curious(X))))&
((~rich(fred))=>((~brave(susan)&generous(susan))))&
(((~creative(fred)|~funny(fred)))<=>(?[X]:((~patient(X)<~>humble(X)))))&
(![X]:((creative(X)|rich(X))=>(curious(X)<~>calm(X))))&
(![X]:((patient(X)<~>~patient(X))<=>(~calm(X)|~rich(X))))&
(![X]:((calm(X)<~>quiet(X))<=>~creative(X)))&
((?[X]:(~kind(X)))=>(?[X]:((~humble(X)<~>~tall(X)))))&
((?[X]:((wise(X)&~creative(X))))=>((patient(fred)|strong(fred))))&
(?[X]:((humble(X)|generous(X))))&
((tall(susan)|~creative(susan)))&
((creative(alice)&~wise(alice)))&
(?[X]:((~kind(X)&~humble(X))))&
(?[X]:((~tall(X)&~patient(X))))&
(?[X]:((~tall(X)&~old(X))))&
((~brave(john)<~>~rich(john)))&
(?[X]:((tall(X)&~strong(X)))) | ~brave(susan) | [
"p3",
"p5",
"p8",
"p9",
"p11",
"p12",
"p13",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 4559250128173653233198543
% SZS output start Proof for 4559250128173653233198543
4. ! [X0] : ((patient(X0) | ~wise(X0)) => (quiet(X0) <~> ~tall(X0))) [input p3]
6. ! [X0] : ((~strong(X0) & ~rich(X0)) <=> (strong(X0) | patient(X0))) [input p5]
9. ! [X0] : ((~tall(X0) & old(X0)) <=> (curious(X0) | ~wise(X0))) [input p8]
10. ~rich(fred) => (generous(susan) & ~brave(susan)) [input p9]
12. ! [X0] : ((rich(X0) | creative(X0)) => (curious(X0) <~> calm(X0))) [input p11]
13. ! [X0] : ((patient(X0) <~> ~patient(X0)) <=> (~rich(X0) | ~calm(X0))) [input p12]
14. ! [X0] : ((calm(X0) <~> quiet(X0)) <=> ~creative(X0)) [input p13]
16. ? [X0] : (~creative(X0) & wise(X0)) => (strong(fred) | patient(fred)) [input p15]
22. ? [X0] : (~old(X0) & ~tall(X0)) [input p21]
25. brave(susan) [input hypothesis]
31. ! [X0] : ((quiet(X0) <~> ~tall(X0)) | (~patient(X0) & wise(X0))) [ennf transformation 4]
34. (generous(susan) & ~brave(susan)) | rich(fred) [ennf transformation 10]
35. ! [X0] : ((curious(X0) <~> calm(X0)) | (~rich(X0) & ~creative(X0))) [ennf transformation 12]
37. (strong(fred) | patient(fred)) | ! [X0] : (creative(X0) | ~wise(X0)) [ennf transformation 16]
38. strong(fred) | patient(fred) | ! [X0] : (creative(X0) | ~wise(X0)) [flattening 37]
47. ! [X0] : (((tall(X0) | ~quiet(X0)) & (~tall(X0) | quiet(X0))) | (~patient(X0) & wise(X0))) [nnf transformation 31]
48. ! [X0] : (((~strong(X0) & ~rich(X0)) | (~strong(X0) & ~patient(X0))) & ((strong(X0) | patient(X0)) | (strong(X0) | rich(X0)))) [nnf transformation 6]
49. ! [X0] : (((~strong(X0) & ~rich(X0)) | (~strong(X0) & ~patient(X0))) & (strong(X0) | patient(X0) | strong(X0) | rich(X0))) [flattening 48]
56. ! [X0] : (((~tall(X0) & old(X0)) | (~curious(X0) & wise(X0))) & ((curious(X0) | ~wise(X0)) | (tall(X0) | ~old(X0)))) [nnf transformation 9]
57. ! [X0] : (((~tall(X0) & old(X0)) | (~curious(X0) & wise(X0))) & (curious(X0) | ~wise(X0) | tall(X0) | ~old(X0))) [flattening 56]
63. ! [X0] : (((~calm(X0) | ~curious(X0)) & (calm(X0) | curious(X0))) | (~rich(X0) & ~creative(X0))) [nnf transformation 35]
64. ! [X0] : ((((patient(X0) | ~patient(X0)) & (~patient(X0) | patient(X0))) | (rich(X0) & calm(X0))) & ((~rich(X0) | ~calm(X0)) | ((patient(X0) | patient(X0)) & (~patient(X0) | ~patient(X0))))) [nnf transformation 13]
65. ! [X0] : ((((patient(X0) | ~patient(X0)) & (~patient(X0) | patient(X0))) | (rich(X0) & calm(X0))) & (~rich(X0) | ~calm(X0) | ((patient(X0) | patient(X0)) & (~patient(X0) | ~patient(X0))))) [flattening 64]
66. ! [X0] : ((((~quiet(X0) | ~calm(X0)) & (quiet(X0) | calm(X0))) | creative(X0)) & (~creative(X0) | ((calm(X0) | ~quiet(X0)) & (quiet(X0) | ~calm(X0))))) [nnf transformation 14]
77. ? [X0] : (~old(X0) & ~tall(X0)) => (~old(sK8) & ~tall(sK8)) [choice axiom]
78. ~old(sK8) & ~tall(sK8) [skolemisation 22,77]
92. ~quiet(X0) | tall(X0) | ~patient(X0) [cnf transformation 47]
95. strong(X0) | patient(X0) | strong(X0) | rich(X0) [cnf transformation 49]
96. ~rich(X0) | ~patient(X0) [cnf transformation 49]
99. ~strong(X0) | ~strong(X0) [cnf transformation 49]
110. old(X0) | wise(X0) [cnf transformation 57]
111. ~curious(X0) | old(X0) [cnf transformation 57]
114. ~brave(susan) | rich(fred) [cnf transformation 34]
122. ~creative(X0) | curious(X0) | calm(X0) [cnf transformation 63]
123. ~rich(X0) | curious(X0) | calm(X0) [cnf transformation 63]
127. ~rich(X0) | ~calm(X0) | patient(X0) | patient(X0) [cnf transformation 65]
132. ~calm(X0) | quiet(X0) | ~creative(X0) [cnf transformation 66]
138. strong(fred) | patient(fred) | creative(X0) | ~wise(X0) [cnf transformation 38]
147. ~tall(sK8) [cnf transformation 78]
148. ~old(sK8) [cnf transformation 78]
153. brave(susan) [cnf transformation 25]
155. ~rich(X0) | ~calm(X0) | patient(X0) [duplicate literal removal 127]
156. strong(X0) | patient(X0) | rich(X0) [duplicate literal removal 95]
157. ~strong(X0) [duplicate literal removal 99]
190. rich(X0) | patient(X0) [subsumption resolution 156,157]
213. 13 <=> rich(fred) [avatar definition]
215. rich(fred) <- (13) [avatar component clause 213]
222. 15 <=> brave(susan) [avatar definition]
225. 13 | ~15 [avatar split clause 114,222,213]
254. ~calm(X0) | ~rich(X0) [subsumption resolution 155,96]
268. patient(fred) | creative(X0) | ~wise(X0) [subsumption resolution 138,157]
270. 25 <=> ! [X0] : (creative(X0) | ~wise(X0)) [avatar definition]
271. ~wise(X0) | creative(X0) <- (25) [avatar component clause 270]
273. 26 <=> patient(fred) [avatar definition]
276. 25 | 26 [avatar split clause 268,273,270]
305. 15 [avatar split clause 153,222]
308. ~patient(fred) <- (13) [resolution 96,215]
309. ~26 | ~13 [avatar split clause 308,213,273]
310. wise(sK8) [resolution 110,148]
315. creative(sK8) <- (25) [resolution 271,310]
376. curious(sK8) | calm(sK8) <- (25) [resolution 122,315]
388. 44 <=> calm(sK8) [avatar definition]
390. calm(sK8) <- (44) [avatar component clause 388]
392. 45 <=> curious(sK8) [avatar definition]
393. ~curious(sK8) <- (~45) [avatar component clause 392]
394. curious(sK8) <- (45) [avatar component clause 392]
395. 44 | 45 | ~25 [avatar split clause 376,270,392,388]
398. calm(X0) | curious(X0) | patient(X0) [resolution 123,190]
507. curious(X4) | patient(X4) | ~rich(X4) [resolution 398,254]
509. ~rich(X4) | curious(X4) [subsumption resolution 507,96]
529. curious(X0) | patient(X0) [resolution 509,190]
531. quiet(sK8) | ~creative(sK8) <- (44) [resolution 390,132]
535. quiet(sK8) <- (25, 44) [subsumption resolution 531,315]
644. patient(sK8) <- (~45) [resolution 529,393]
670. tall(sK8) | ~patient(sK8) <- (25, 44) [resolution 535,92]
672. ~patient(sK8) <- (25, 44) [subsumption resolution 670,147]
673. $false <- (25, 44, ~45) [subsumption resolution 672,644]
674. ~25 | ~44 | 45 [avatar contradiction clause 673]
684. old(sK8) <- (45) [resolution 394,111]
694. $false <- (45) [subsumption resolution 684,148]
695. ~45 [avatar contradiction clause 694]
696. $false [avatar sat refutation 225,276,305,309,395,674,695]
% SZS output end Proof for 4559250128173653233198543
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is funny is not rich and vice versa.
Everyone who is not generous is either not patient or not strong and vice versa.
If someone is both tall and not calm then alice is both strong and old.
If alice is both kind and not tall then john is both not rich and not generous and vice versa.
If someone is not strong or not calm then alice is rich and vice versa.
Everyone who is generous is rich or not generous.
If lucy is creative or rich then alice is either funny or wise and vice versa.
If alice is creative or not rich then someone is both rich and not old and vice versa.
Everyone who is either happy or generous is either creative or not rich and vice versa.
Everyone who is both funny and not calm is both not quiet and curious.
Everyone who is rich or not happy is brave.
If someone is wise then susan is both not generous and happy.
Everyone who is not strong is either happy or creative and vice versa.
If someone is both not funny and not wise then john is both not calm and not curious.
Everyone who is tall is either not curious or rich.
If someone is brave then someone is both tall and not funny and vice versa.
Someone is both kind and not wise.
John is both kind and rich.
Someone is tall or brave.
Mary is not brave or old.
Someone is happy or not patient.
Someone is both not quiet and creative.
Someone is not curious or not patient.
Mary is both not calm and not wise. | Alice is not patient. | entailment | (![X]:(funny(X)<=>~rich(X)))&
(![X]:(~generous(X)<=>(~patient(X)<~>~strong(X))))&
((?[X]:((tall(X)&~calm(X))))=>((strong(alice)&old(alice))))&
(((kind(alice)&~tall(alice)))<=>((~rich(john)&~generous(john))))&
((?[X]:((~strong(X)|~calm(X))))<=>(rich(alice)))&
(![X]:(generous(X)=>(rich(X)|~generous(X))))&
(((creative(lucy)|rich(lucy)))<=>((funny(alice)<~>wise(alice))))&
(((creative(alice)|~rich(alice)))<=>(?[X]:((rich(X)&~old(X)))))&
(![X]:((happy(X)<~>generous(X))<=>(creative(X)<~>~rich(X))))&
(![X]:((funny(X)&~calm(X))=>(~quiet(X)&curious(X))))&
(![X]:((rich(X)|~happy(X))=>brave(X)))&
((?[X]:(wise(X)))=>((~generous(susan)&happy(susan))))&
(![X]:(~strong(X)<=>(happy(X)<~>creative(X))))&
((?[X]:((~funny(X)&~wise(X))))=>((~calm(john)&~curious(john))))&
(![X]:(tall(X)=>(~curious(X)<~>rich(X))))&
((?[X]:(brave(X)))<=>(?[X]:((tall(X)&~funny(X)))))&
(?[X]:((kind(X)&~wise(X))))&
((kind(john)&rich(john)))&
(?[X]:((tall(X)|brave(X))))&
((~brave(mary)|old(mary)))&
(?[X]:((happy(X)|~patient(X))))&
(?[X]:((~quiet(X)&creative(X))))&
(?[X]:((~curious(X)|~patient(X))))&
((~calm(mary)&~wise(mary))) | ~patient(alice) | [
"p1",
"p4",
"p5",
"p8",
"p12",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 5393804825349673985468702
% SZS output start Proof for 5393804825349673985468702
2. ! [X0] : (~generous(X0) <=> (~patient(X0) <~> ~strong(X0))) [input p1]
5. ? [X0] : (~calm(X0) | ~strong(X0)) <=> rich(alice) [input p4]
6. ! [X0] : (generous(X0) => (~generous(X0) | rich(X0))) [input p5]
9. ! [X0] : ((happy(X0) <~> generous(X0)) <=> (creative(X0) <~> ~rich(X0))) [input p8]
13. ! [X0] : (~strong(X0) <=> (happy(X0) <~> creative(X0))) [input p12]
24. ~wise(mary) & ~calm(mary) [input p23]
25. patient(alice) [input hypothesis]
30. ! [X0] : ((~generous(X0) | rich(X0)) | ~generous(X0)) [ennf transformation 6]
31. ! [X0] : (~generous(X0) | rich(X0) | ~generous(X0)) [flattening 30]
39. ! [X0] : ((~generous(X0) | ((~patient(X0) | strong(X0)) & (~strong(X0) | patient(X0)))) & (((strong(X0) | patient(X0)) & (~strong(X0) | ~patient(X0))) | generous(X0))) [nnf transformation 2]
42. (? [X0] : (~calm(X0) | ~strong(X0)) | ~rich(alice)) & (rich(alice) | ! [X0] : (calm(X0) & strong(X0))) [nnf transformation 5]
43. (? [X0] : (~calm(X0) | ~strong(X0)) | ~rich(alice)) & (rich(alice) | ! [X1] : (calm(X1) & strong(X1))) [rectify 42]
44. ? [X0] : (~calm(X0) | ~strong(X0)) => (~calm(sK0) | ~strong(sK0)) [choice axiom]
45. ((~calm(sK0) | ~strong(sK0)) | ~rich(alice)) & (rich(alice) | ! [X1] : (calm(X1) & strong(X1))) [skolemisation 43,44]
53. ! [X0] : ((((~generous(X0) | ~happy(X0)) & (generous(X0) | happy(X0))) | ((creative(X0) | rich(X0)) & (~rich(X0) | ~creative(X0)))) & (((rich(X0) | ~creative(X0)) & (~rich(X0) | creative(X0))) | ((happy(X0) | ~generous(X0)) & (generous(X0) | ~happy(X0))))) [nnf transformation 9]
54. ! [X0] : ((~strong(X0) | ((happy(X0) | ~creative(X0)) & (creative(X0) | ~happy(X0)))) & (((~creative(X0) | ~happy(X0)) & (creative(X0) | happy(X0))) | strong(X0))) [nnf transformation 13]
73. ~strong(X0) | ~patient(X0) | generous(X0) [cnf transformation 39]
76. ~patient(X0) | ~generous(X0) | strong(X0) [cnf transformation 39]
84. rich(alice) | calm(X1) [cnf transformation 45]
86. ~generous(X0) | rich(X0) | ~generous(X0) [cnf transformation 31]
98. ~happy(X0) | creative(X0) | generous(X0) | ~rich(X0) [cnf transformation 53]
99. ~rich(X0) | creative(X0) | happy(X0) | ~generous(X0) [cnf transformation 53]
102. ~creative(X0) | happy(X0) | ~rich(X0) | generous(X0) [cnf transformation 53]
104. ~generous(X0) | ~happy(X0) | ~rich(X0) | ~creative(X0) [cnf transformation 53]
111. happy(X0) | creative(X0) | strong(X0) [cnf transformation 54]
112. ~happy(X0) | ~creative(X0) | strong(X0) [cnf transformation 54]
113. ~happy(X0) | creative(X0) | ~strong(X0) [cnf transformation 54]
114. ~creative(X0) | happy(X0) | ~strong(X0) [cnf transformation 54]
131. ~calm(mary) [cnf transformation 24]
133. patient(alice) [cnf transformation 25]
134. ~generous(X0) | rich(X0) [duplicate literal removal 86]
144. 3 <=> strong(alice) [avatar definition]
145. ~strong(alice) <- (~3) [avatar component clause 144]
146. strong(alice) <- (3) [avatar component clause 144]
169. 8 <=> rich(alice) [avatar definition]
170. rich(alice) <- (8) [avatar component clause 169]
182. 11 <=> ! [X1] : calm(X1) [avatar definition]
183. calm(X1) <- (11) [avatar component clause 182]
184. 11 | 8 [avatar split clause 84,169,182]
215. 18 <=> creative(alice) [avatar definition]
216. ~creative(alice) <- (~18) [avatar component clause 215]
217. creative(alice) <- (18) [avatar component clause 215]
231. ~happy(X0) | ~generous(X0) | ~creative(X0) [subsumption resolution 104,134]
234. ~generous(X0) | happy(X0) | creative(X0) [subsumption resolution 99,134]
339. ~patient(alice) | generous(alice) <- (3) [resolution 73,146]
340. generous(alice) <- (3) [subsumption resolution 339,133]
348. ~generous(alice) | strong(alice) [resolution 76,133]
368. $false <- (11) [resolution 183,131]
373. ~11 [avatar contradiction clause 368]
398. happy(alice) | ~strong(alice) <- (18) [resolution 114,217]
400. happy(alice) <- (3, 18) [subsumption resolution 398,146]
435. ~generous(alice) | ~creative(alice) <- (3, 18) [resolution 400,231]
438. ~creative(alice) <- (3, 18) [subsumption resolution 435,340]
439. $false <- (3, 18) [subsumption resolution 438,217]
440. ~3 | ~18 [avatar contradiction clause 439]
459. happy(alice) | creative(alice) <- (3) [resolution 234,340]
460. happy(alice) <- (3, ~18) [subsumption resolution 459,216]
465. creative(X1) | generous(X1) | ~rich(X1) | creative(X1) | strong(X1) [resolution 98,111]
469. ~rich(X1) | generous(X1) | creative(X1) | strong(X1) [duplicate literal removal 465]
580. creative(alice) | ~strong(alice) <- (3, ~18) [resolution 460,113]
582. ~strong(alice) <- (3, ~18) [subsumption resolution 580,216]
583. $false <- (3, ~18) [subsumption resolution 582,146]
584. ~3 | 18 [avatar contradiction clause 583]
586. 59 <=> generous(alice) [avatar definition]
588. ~generous(alice) <- (~59) [avatar component clause 586]
589. 3 | ~59 [avatar split clause 348,586,144]
595. generous(alice) | creative(alice) | strong(alice) <- (8) [resolution 469,170]
602. creative(alice) | strong(alice) <- (8, ~59) [subsumption resolution 595,588]
665. creative(alice) <- (~3, 8, ~59) [subsumption resolution 602,145]
666. 18 | 3 | ~8 | 59 [avatar split clause 665,586,169,144,215]
685. happy(alice) | ~rich(alice) | generous(alice) <- (18) [resolution 217,102]
687. happy(alice) | generous(alice) <- (8, 18) [subsumption resolution 685,170]
688. happy(alice) <- (8, 18, ~59) [subsumption resolution 687,588]
696. ~creative(alice) | strong(alice) <- (8, 18, ~59) [resolution 688,112]
697. strong(alice) <- (8, 18, ~59) [subsumption resolution 696,217]
698. $false <- (~3, 8, 18, ~59) [subsumption resolution 697,145]
699. 3 | ~8 | ~18 | 59 [avatar contradiction clause 698]
700. $false [avatar sat refutation 184,373,440,584,589,666,699]
% SZS output end Proof for 5393804825349673985468702
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5373
% Time elapsed: 0.023 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not generous is both wise and not brave.
Everyone who is both not funny and not brave is both kind and not tall.
If someone is not strong then john is either not creative or not funny and vice versa.
If fred is either quiet or not tall then mary is either not funny or quiet.
Everyone who is not old or not strong is both curious and calm and vice versa.
If someone is either not wise or generous then someone is either kind or not old and vice versa.
If someone is humble then susan is old or not tall and vice versa.
Everyone who is both tall and patient is tall or not rich.
Everyone who is not happy or not curious is curious or not humble.
If someone is not funny then paul is old.
Everyone who is either rich or not quiet is calm or not generous.
If someone is either not tall or not strong then someone is rich and vice versa.
Everyone who is kind is either quiet or not calm and vice versa.
Everyone who is either tall or quiet is not curious.
Everyone who is either happy or strong is tall.
Everyone who is curious is both not calm and not tall.
Someone is not curious or not funny.
Susan is not strong or wise.
Someone is wise or not curious.
Someone is both brave and not wise.
Someone is kind.
Paul is not strong or generous.
Lucy is both happy and not wise.
Paul is creative or not rich. | Paul is not generous. | contradiction | (![X]:(~generous(X)=>(wise(X)&~brave(X))))&
(![X]:((~funny(X)&~brave(X))=>(kind(X)&~tall(X))))&
((?[X]:(~strong(X)))<=>((~creative(john)<~>~funny(john))))&
(((quiet(fred)<~>~tall(fred)))=>((~funny(mary)<~>quiet(mary))))&
(![X]:((~old(X)|~strong(X))<=>(curious(X)&calm(X))))&
((?[X]:((~wise(X)<~>generous(X))))<=>(?[X]:((kind(X)<~>~old(X)))))&
((?[X]:(humble(X)))<=>((old(susan)|~tall(susan))))&
(![X]:((tall(X)&patient(X))=>(tall(X)|~rich(X))))&
(![X]:((~happy(X)|~curious(X))=>(curious(X)|~humble(X))))&
((?[X]:(~funny(X)))=>(old(paul)))&
(![X]:((rich(X)<~>~quiet(X))=>(calm(X)|~generous(X))))&
((?[X]:((~tall(X)<~>~strong(X))))<=>(?[X]:(rich(X))))&
(![X]:(kind(X)<=>(quiet(X)<~>~calm(X))))&
(![X]:((tall(X)<~>quiet(X))=>~curious(X)))&
(![X]:((happy(X)<~>strong(X))=>tall(X)))&
(![X]:(curious(X)=>(~calm(X)&~tall(X))))&
(?[X]:((~curious(X)|~funny(X))))&
((~strong(susan)|wise(susan)))&
(?[X]:((wise(X)|~curious(X))))&
(?[X]:((brave(X)&~wise(X))))&
(?[X]:(kind(X)))&
((~strong(paul)|generous(paul)))&
((happy(lucy)&~wise(lucy)))&
((creative(paul)|~rich(paul))) | ~generous(paul) | [
"p4",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 2924514493330365859960512
% SZS output start Proof for 2924514493330365859960512
5. ! [X0] : ((~strong(X0) | ~old(X0)) <=> (calm(X0) & curious(X0))) [input p4]
16. ! [X0] : (curious(X0) => (~tall(X0) & ~calm(X0))) [input p15]
22. generous(paul) | ~strong(paul) [input p21]
25. ~generous(paul) [input hypothesis]
40. ! [X0] : ((~tall(X0) & ~calm(X0)) | ~curious(X0)) [ennf transformation 16]
46. ! [X0] : (((~strong(X0) | ~old(X0)) | (~calm(X0) | ~curious(X0))) & ((calm(X0) & curious(X0)) | (strong(X0) & old(X0)))) [nnf transformation 5]
47. ! [X0] : ((~strong(X0) | ~old(X0) | ~calm(X0) | ~curious(X0)) & ((calm(X0) & curious(X0)) | (strong(X0) & old(X0)))) [flattening 46]
88. curious(X0) | strong(X0) [cnf transformation 47]
90. calm(X0) | strong(X0) [cnf transformation 47]
120. ~calm(X0) | ~curious(X0) [cnf transformation 40]
128. generous(paul) | ~strong(paul) [cnf transformation 22]
132. ~generous(paul) [cnf transformation 25]
149. 4 <=> ! [X1] : strong(X1) [avatar definition]
150. strong(X1) <- (4) [avatar component clause 149]
287. 34 <=> strong(paul) [avatar definition]
289. ~strong(paul) <- (~34) [avatar component clause 287]
291. 35 <=> generous(paul) [avatar definition]
294. ~34 | 35 [avatar split clause 128,291,287]
304. ~35 [avatar split clause 132,291]
316. ~curious(X0) | strong(X0) [resolution 120,90]
318. strong(X0) [subsumption resolution 316,88]
319. 4 [avatar split clause 318,149]
322. $false <- (4, ~34) [resolution 150,289]
327. ~4 | 34 [avatar contradiction clause 322]
329. $false [avatar sat refutation 294,304,319,327]
% SZS output end Proof for 2924514493330365859960512
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
If someone is not strong or not creative then john is both not creative and not tall and vice versa.
Everyone who is not humble is not quiet or patient.
If someone is not brave then someone is both calm and strong and vice versa.
If someone is generous or patient then someone is wise or not quiet.
Everyone who is not brave is both strong and not funny and vice versa.
If fred is not brave then someone is both not wise and not quiet and vice versa.
If someone is both calm and not happy then mary is either not calm or not quiet and vice versa.
Everyone who is not creative is not calm or not humble and vice versa.
If john is either not patient or happy then lucy is both not quiet and not brave and vice versa.
If someone is not brave then someone is both not tall and not generous and vice versa.
If lucy is not tall then susan is patient or not curious and vice versa.
Everyone who is not wise or not creative is both not brave and funny.
If alice is not wise or calm then john is both not kind and old.
Everyone who is not patient is both not creative and not old.
Everyone who is both brave and not humble is not tall.
Everyone who is happy or curious is either not calm or old.
John is either not happy or not calm.
Alice is not tall.
Mary is either tall or generous.
Someone is either not rich or creative.
Someone is either tall or funny.
Someone is either not generous or humble. | Lucy is not funny. | neutral | ((?[X]:((~strong(X)|~creative(X))))<=>((~creative(john)&~tall(john))))&
(![X]:(~humble(X)=>(~quiet(X)|patient(X))))&
((?[X]:(~brave(X)))<=>(?[X]:((calm(X)&strong(X)))))&
((?[X]:((generous(X)|patient(X))))=>(?[X]:((wise(X)|~quiet(X)))))&
(![X]:(~brave(X)<=>(strong(X)&~funny(X))))&
((~brave(fred))<=>(?[X]:((~wise(X)&~quiet(X)))))&
((?[X]:((calm(X)&~happy(X))))<=>((~calm(mary)<~>~quiet(mary))))&
(![X]:(~creative(X)<=>(~calm(X)|~humble(X))))&
(((~patient(john)<~>happy(john)))<=>((~quiet(lucy)&~brave(lucy))))&
((?[X]:(~brave(X)))<=>(?[X]:((~tall(X)&~generous(X)))))&
((~tall(lucy))<=>((patient(susan)|~curious(susan))))&
(![X]:((~wise(X)|~creative(X))=>(~brave(X)&funny(X))))&
(((~wise(alice)|calm(alice)))=>((~kind(john)&old(john))))&
(![X]:(~patient(X)=>(~creative(X)&~old(X))))&
(![X]:((brave(X)&~humble(X))=>~tall(X)))&
(![X]:((happy(X)|curious(X))=>(~calm(X)<~>old(X))))&
((~happy(john)<~>~calm(john)))&
(~tall(alice))&
((tall(mary)<~>generous(mary)))&
(?[X]:((~rich(X)<~>creative(X))))&
(?[X]:((tall(X)<~>funny(X))))&
(?[X]:((~generous(X)<~>humble(X)))) | ~funny(lucy) | [] | null | 0 |
Everyone who is not curious is not happy and vice versa.
Everyone who is not creative or tall is both not quiet and quiet and vice versa.
If someone is either not creative or happy then someone is not creative or happy and vice versa.
Everyone who is either not happy or quiet is tall and vice versa.
Everyone who is rich is either old or not tall.
If someone is tall or not curious then fred is both not wise and kind and vice versa.
If mary is either quiet or funny then alice is humble or not happy.
Everyone who is both not creative and not brave is both not happy and strong and vice versa.
Everyone who is creative is not rich or not humble and vice versa.
Everyone who is both curious and not curious is strong.
If susan is not happy or funny then mary is not strong and vice versa.
If susan is both not curious and patient then someone is both not strong and generous.
Everyone who is not wise is wise.
If fred is either strong or humble then someone is not strong or not quiet and vice versa.
Everyone who is not rich or not quiet is patient.
Everyone who is either not kind or wise is not old.
Alice is curious.
Someone is brave or not brave.
Lucy is both strong and happy.
Fred is either not kind or patient.
Someone is either old or not creative.
Alice is old or not patient. | Alice is not quiet. | entailment | (![X]:(~curious(X)<=>~happy(X)))&
(![X]:((~creative(X)|tall(X))<=>(~quiet(X)&quiet(X))))&
((?[X]:((~creative(X)<~>happy(X))))<=>(?[X]:((~creative(X)|happy(X)))))&
(![X]:((~happy(X)<~>quiet(X))<=>tall(X)))&
(![X]:(rich(X)=>(old(X)<~>~tall(X))))&
((?[X]:((tall(X)|~curious(X))))<=>((~wise(fred)&kind(fred))))&
(((quiet(mary)<~>funny(mary)))=>((humble(alice)|~happy(alice))))&
(![X]:((~creative(X)&~brave(X))<=>(~happy(X)&strong(X))))&
(![X]:(creative(X)<=>(~rich(X)|~humble(X))))&
(![X]:((curious(X)&~curious(X))=>strong(X)))&
(((~happy(susan)|funny(susan)))<=>(~strong(mary)))&
(((~curious(susan)&patient(susan)))=>(?[X]:((~strong(X)&generous(X)))))&
(![X]:(~wise(X)=>wise(X)))&
(((strong(fred)<~>humble(fred)))<=>(?[X]:((~strong(X)|~quiet(X)))))&
(![X]:((~rich(X)|~quiet(X))=>patient(X)))&
(![X]:((~kind(X)<~>wise(X))=>~old(X)))&
(curious(alice))&
(?[X]:((brave(X)|~brave(X))))&
((strong(lucy)&happy(lucy)))&
((~kind(fred)<~>patient(fred)))&
(?[X]:((old(X)<~>~creative(X))))&
((old(alice)|~patient(alice))) | ~quiet(alice) | [
"p0",
"p1",
"p3",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 9192052262056239575991696
% SZS output start Proof for 9192052262056239575991696
1. ! [X0] : (~curious(X0) <=> ~happy(X0)) [input p0]
2. ! [X0] : ((tall(X0) | ~creative(X0)) <=> (quiet(X0) & ~quiet(X0))) [input p1]
4. ! [X0] : ((~happy(X0) <~> quiet(X0)) <=> tall(X0)) [input p3]
17. curious(alice) [input p16]
23. quiet(alice) [input hypothesis]
36. ! [X0] : ((~curious(X0) | happy(X0)) & (~happy(X0) | curious(X0))) [nnf transformation 1]
37. ! [X0] : (((tall(X0) | ~creative(X0)) | (~quiet(X0) | quiet(X0))) & ((quiet(X0) & ~quiet(X0)) | (~tall(X0) & creative(X0)))) [nnf transformation 2]
38. ! [X0] : ((tall(X0) | ~creative(X0) | ~quiet(X0) | quiet(X0)) & ((quiet(X0) & ~quiet(X0)) | (~tall(X0) & creative(X0)))) [flattening 37]
44. ! [X0] : ((((~quiet(X0) | happy(X0)) & (quiet(X0) | ~happy(X0))) | ~tall(X0)) & (tall(X0) | ((~happy(X0) | ~quiet(X0)) & (quiet(X0) | happy(X0))))) [nnf transformation 4]
72. ~curious(X0) | happy(X0) [cnf transformation 36]
74. ~quiet(X0) | ~tall(X0) [cnf transformation 38]
76. ~tall(X0) | quiet(X0) [cnf transformation 38]
85. tall(X0) | ~happy(X0) | ~quiet(X0) [cnf transformation 44]
120. curious(alice) [cnf transformation 17]
129. quiet(alice) [cnf transformation 23]
131. ~tall(X0) [subsumption resolution 74,76]
149. ~quiet(X0) | ~happy(X0) [subsumption resolution 85,131]
184. 11 <=> happy(alice) [avatar definition]
186. ~happy(alice) <- (~11) [avatar component clause 184]
267. happy(alice) [resolution 72,120]
269. $false <- (~11) [subsumption resolution 267,186]
270. 11 [avatar contradiction clause 269]
281. ~happy(alice) [resolution 149,129]
285. ~11 [avatar split clause 281,184]
288. $false [avatar sat refutation 270,285]
% SZS output end Proof for 9192052262056239575991696
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.025 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both not calm and happy then lucy is both not quiet and generous and vice versa.
Everyone who is not humble is either not tall or old and vice versa.
Everyone who is either generous or humble is both humble and not calm and vice versa.
Everyone who is brave is both not rich and not tall and vice versa.
Everyone who is both patient and old is tall or rich.
Everyone who is not wise or not tall is curious or humble.
If mary is kind then paul is not quiet and vice versa.
If someone is either generous or not curious then fred is not humble and vice versa.
Everyone who is wise or strong is either not old or not tall.
If someone is curious then someone is not humble and vice versa.
If alice is not quiet then alice is not old or rich and vice versa.
Everyone who is rich is not creative or not tall and vice versa.
Everyone who is both not creative and not tall is rich and vice versa.
If someone is either funny or not humble then susan is creative or not wise.
Everyone who is both brave and creative is either brave or tall and vice versa.
If fred is kind then someone is either calm or not humble.
John is both calm and old.
Someone is both rich and not creative.
Someone is both not kind and wise.
Susan is not quiet or generous.
Susan is either not funny or brave.
Someone is either not wise or tall.
Someone is funny.
John is either calm or not old. | Fred is quiet. | neutral | ((?[X]:((~calm(X)&happy(X))))<=>((~quiet(lucy)&generous(lucy))))&
(![X]:(~humble(X)<=>(~tall(X)<~>old(X))))&
(![X]:((generous(X)<~>humble(X))<=>(humble(X)&~calm(X))))&
(![X]:(brave(X)<=>(~rich(X)&~tall(X))))&
(![X]:((patient(X)&old(X))=>(tall(X)|rich(X))))&
(![X]:((~wise(X)|~tall(X))=>(curious(X)|humble(X))))&
((kind(mary))<=>(~quiet(paul)))&
((?[X]:((generous(X)<~>~curious(X))))<=>(~humble(fred)))&
(![X]:((wise(X)|strong(X))=>(~old(X)<~>~tall(X))))&
((?[X]:(curious(X)))<=>(?[X]:(~humble(X))))&
((~quiet(alice))<=>((~old(alice)|rich(alice))))&
(![X]:(rich(X)<=>(~creative(X)|~tall(X))))&
(![X]:((~creative(X)&~tall(X))<=>rich(X)))&
((?[X]:((funny(X)<~>~humble(X))))=>((creative(susan)|~wise(susan))))&
(![X]:((brave(X)&creative(X))<=>(brave(X)<~>tall(X))))&
((kind(fred))=>(?[X]:((calm(X)<~>~humble(X)))))&
((calm(john)&old(john)))&
(?[X]:((rich(X)&~creative(X))))&
(?[X]:((~kind(X)&wise(X))))&
((~quiet(susan)|generous(susan)))&
((~funny(susan)<~>brave(susan)))&
(?[X]:((~wise(X)<~>tall(X))))&
(?[X]:(funny(X)))&
((calm(john)<~>~old(john))) | quiet(fred) | [] | null | 0 |
If fred is not rich then someone is wise. If someone is calm then paul is generous and vice versa. If someone is happy then alice is both old and not calm. Everyone who is generous or not funny is not creative. If someone is either happy or funny then susan is both generous and happy and vice versa. If someone is old then lucy is both rich and not rich and vice versa. Everyone who is both humble and not kind is both not calm and not patient and vice versa. Everyone who is wise or not kind is either wise or not curious. If someone is either happy or not humble then someone is either not brave or creative and vice versa. If paul is not funny then john is either not tall or quiet. If someone is brave or not brave then someone is either not kind or not generous and vice versa. Everyone who is both generous and curious is not generous or not strong. If john is both curious and old then mary is old or creative. If john is either brave or not creative then mary is either brave or old and vice versa. If susan is either funny or curious then fred is kind or humble. Someone is happy or not patient. Someone is either quiet or not creative. Someone is both not brave and not wise. Someone is brave or patient. Someone is not curious. Someone is either not happy or brave. | Lucy is creative. | contradiction | ((~rich(fred))=>(?[X]:(wise(X))))&
((?[X]:(calm(X)))<=>(generous(paul)))&
((?[X]:(happy(X)))=>((old(alice)&~calm(alice))))&
(![X]:((generous(X)|~funny(X))=>~creative(X)))&
((?[X]:((happy(X)<~>funny(X))))<=>((generous(susan)&happy(susan))))&
((?[X]:(old(X)))<=>((rich(lucy)&~rich(lucy))))&
(![X]:((humble(X)&~kind(X))<=>(~calm(X)&~patient(X))))&
(![X]:((wise(X)|~kind(X))=>(wise(X)<~>~curious(X))))&
((?[X]:((happy(X)<~>~humble(X))))<=>(?[X]:((~brave(X)<~>creative(X)))))&
((~funny(paul))=>((~tall(john)<~>quiet(john))))&
((?[X]:((brave(X)|~brave(X))))<=>(?[X]:((~kind(X)<~>~generous(X)))))&
(![X]:((generous(X)&curious(X))=>(~generous(X)|~strong(X))))&
(((curious(john)&old(john)))=>((old(mary)|creative(mary))))&
(((brave(john)<~>~creative(john)))<=>((brave(mary)<~>old(mary))))&
(((funny(susan)<~>curious(susan)))=>((kind(fred)|humble(fred))))&
(?[X]:((happy(X)|~patient(X))))&
(?[X]:((quiet(X)<~>~creative(X))))&
(?[X]:((~brave(X)&~wise(X))))&
(?[X]:((brave(X)|patient(X))))&
(?[X]:(~curious(X)))&
(?[X]:((~happy(X)<~>brave(X)))) | creative(lucy) | [
"p2",
"p3",
"p4",
"p5",
"hypothesis"
] | % SZS status Unsatisfiable for 4749815409562106048832074
% SZS output start Proof for 4749815409562106048832074
3. ? [X0] : happy(X0) => (~calm(alice) & old(alice)) [input p2]
4. ! [X0] : ((~funny(X0) | generous(X0)) => ~creative(X0)) [input p3]
5. ? [X0] : (happy(X0) <~> funny(X0)) <=> (happy(susan) & generous(susan)) [input p4]
6. ? [X0] : old(X0) <=> (~rich(lucy) & rich(lucy)) [input p5]
22. creative(lucy) [input hypothesis]
27. (~calm(alice) & old(alice)) | ! [X0] : ~happy(X0) [ennf transformation 3]
28. ! [X0] : (~creative(X0) | (funny(X0) & ~generous(X0))) [ennf transformation 4]
41. (? [X0] : ((~funny(X0) | ~happy(X0)) & (funny(X0) | happy(X0))) | (~happy(susan) | ~generous(susan))) & ((happy(susan) & generous(susan)) | ! [X0] : ((happy(X0) | ~funny(X0)) & (funny(X0) | ~happy(X0)))) [nnf transformation 5]
42. (? [X0] : ((~funny(X0) | ~happy(X0)) & (funny(X0) | happy(X0))) | ~happy(susan) | ~generous(susan)) & ((happy(susan) & generous(susan)) | ! [X0] : ((happy(X0) | ~funny(X0)) & (funny(X0) | ~happy(X0)))) [flattening 41]
43. (? [X0] : ((~funny(X0) | ~happy(X0)) & (funny(X0) | happy(X0))) | ~happy(susan) | ~generous(susan)) & ((happy(susan) & generous(susan)) | ! [X1] : ((happy(X1) | ~funny(X1)) & (funny(X1) | ~happy(X1)))) [rectify 42]
44. ? [X0] : ((~funny(X0) | ~happy(X0)) & (funny(X0) | happy(X0))) => ((~funny(sK2) | ~happy(sK2)) & (funny(sK2) | happy(sK2))) [choice axiom]
45. (((~funny(sK2) | ~happy(sK2)) & (funny(sK2) | happy(sK2))) | ~happy(susan) | ~generous(susan)) & ((happy(susan) & generous(susan)) | ! [X1] : ((happy(X1) | ~funny(X1)) & (funny(X1) | ~happy(X1)))) [skolemisation 43,44]
46. (? [X0] : old(X0) | (rich(lucy) | ~rich(lucy))) & ((~rich(lucy) & rich(lucy)) | ! [X0] : ~old(X0)) [nnf transformation 6]
47. (? [X0] : old(X0) | rich(lucy) | ~rich(lucy)) & ((~rich(lucy) & rich(lucy)) | ! [X0] : ~old(X0)) [flattening 46]
48. (? [X0] : old(X0) | rich(lucy) | ~rich(lucy)) & ((~rich(lucy) & rich(lucy)) | ! [X1] : ~old(X1)) [rectify 47]
49. ? [X0] : old(X0) => old(sK3) [choice axiom]
50. (old(sK3) | rich(lucy) | ~rich(lucy)) & ((~rich(lucy) & rich(lucy)) | ! [X1] : ~old(X1)) [skolemisation 48,49]
84. old(alice) | ~happy(X0) [cnf transformation 27]
87. ~creative(X0) | funny(X0) [cnf transformation 28]
91. happy(susan) | happy(X1) | ~funny(X1) [cnf transformation 45]
94. rich(lucy) | ~old(X1) [cnf transformation 50]
95. ~rich(lucy) | ~old(X1) [cnf transformation 50]
141. creative(lucy) [cnf transformation 22]
166. 6 <=> ! [X0] : ~happy(X0) [avatar definition]
167. ~happy(X0) <- (6) [avatar component clause 166]
174. 8 <=> old(alice) [avatar definition]
176. old(alice) <- (8) [avatar component clause 174]
177. 6 | 8 [avatar split clause 84,174,166]
183. 10 <=> happy(susan) [avatar definition]
184. happy(susan) <- (10) [avatar component clause 183]
197. 13 <=> ! [X1] : (happy(X1) | ~funny(X1)) [avatar definition]
198. ~funny(X1) | happy(X1) <- (13) [avatar component clause 197]
199. 13 | 10 [avatar split clause 91,183,197]
207. 15 <=> ! [X1] : ~old(X1) [avatar definition]
208. ~old(X1) <- (15) [avatar component clause 207]
210. 16 <=> rich(lucy) [avatar definition]
213. 15 | ~16 [avatar split clause 95,210,207]
214. 15 | 16 [avatar split clause 94,210,207]
376. $false <- (6, 10) [resolution 184,167]
377. ~6 | ~10 [avatar contradiction clause 376]
378. $false <- (8, 15) [subsumption resolution 176,208]
379. ~8 | ~15 [avatar contradiction clause 378]
385. funny(lucy) [resolution 87,141]
387. happy(lucy) <- (13) [resolution 198,385]
388. $false <- (6, 13) [subsumption resolution 387,167]
389. ~6 | ~13 [avatar contradiction clause 388]
390. $false [avatar sat refutation 177,199,213,214,377,379,389]
% SZS output end Proof for 4749815409562106048832074
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.039 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both not quiet and funny is both strong and not generous and vice versa. If paul is rich then lucy is either not strong or not quiet. Everyone who is either wise or not generous is either calm or not curious. Everyone who is rich or creative is strong. Everyone who is not generous or calm is both calm and funny and vice versa. If paul is either not rich or not kind then someone is either generous or not tall and vice versa. Everyone who is both calm and patient is either not calm or not kind. Everyone who is quiet is not humble. Everyone who is both not funny and not strong is either not old or not creative and vice versa. If mary is both strong and brave then mary is both not strong and tall and vice versa. Everyone who is both not strong and not tall is not rich or not curious and vice versa. If someone is wise or creative then someone is rich and vice versa. Everyone who is both wise and not calm is not generous or creative and vice versa. If someone is both patient and not humble then susan is either not happy or not strong and vice versa. If lucy is either tall or not generous then someone is not creative. Everyone who is either patient or not old is either not old or not humble. Paul is not brave or not wise. Mary is not strong or not tall. Someone is either not funny or humble. John is either not kind or not happy. Lucy is brave or kind. Susan is not patient or not quiet. Someone is not wise. Someone is both not strong and curious. | Susan is not calm. | entailment | (![X]:((~quiet(X)&funny(X))<=>(strong(X)&~generous(X))))&
((rich(paul))=>((~strong(lucy)<~>~quiet(lucy))))&
(![X]:((wise(X)<~>~generous(X))=>(calm(X)<~>~curious(X))))&
(![X]:((rich(X)|creative(X))=>strong(X)))&
(![X]:((~generous(X)|calm(X))<=>(calm(X)&funny(X))))&
(((~rich(paul)<~>~kind(paul)))<=>(?[X]:((generous(X)<~>~tall(X)))))&
(![X]:((calm(X)&patient(X))=>(~calm(X)<~>~kind(X))))&
(![X]:(quiet(X)=>~humble(X)))&
(![X]:((~funny(X)&~strong(X))<=>(~old(X)<~>~creative(X))))&
(((strong(mary)&brave(mary)))<=>((~strong(mary)&tall(mary))))&
(![X]:((~strong(X)&~tall(X))<=>(~rich(X)|~curious(X))))&
((?[X]:((wise(X)|creative(X))))<=>(?[X]:(rich(X))))&
(![X]:((wise(X)&~calm(X))<=>(~generous(X)|creative(X))))&
((?[X]:((patient(X)&~humble(X))))<=>((~happy(susan)<~>~strong(susan))))&
(((tall(lucy)<~>~generous(lucy)))=>(?[X]:(~creative(X))))&
(![X]:((patient(X)<~>~old(X))=>(~old(X)<~>~humble(X))))&
((~brave(paul)|~wise(paul)))&
((~strong(mary)|~tall(mary)))&
(?[X]:((~funny(X)<~>humble(X))))&
((~kind(john)<~>~happy(john)))&
((brave(lucy)|kind(lucy)))&
((~patient(susan)|~quiet(susan)))&
(?[X]:(~wise(X)))&
(?[X]:((~strong(X)&curious(X)))) | ~calm(susan) | [
"p0",
"p4",
"p7",
"p8",
"p12",
"p15",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 798665042790823080872911
% SZS output start Proof for 798665042790823080872911
1. ! [X0] : ((funny(X0) & ~quiet(X0)) <=> (~generous(X0) & strong(X0))) [input p0]
5. ! [X0] : ((calm(X0) | ~generous(X0)) <=> (funny(X0) & calm(X0))) [input p4]
8. ! [X0] : (quiet(X0) => ~humble(X0)) [input p7]
9. ! [X0] : ((~strong(X0) & ~funny(X0)) <=> (~old(X0) <~> ~creative(X0))) [input p8]
13. ! [X0] : ((~calm(X0) & wise(X0)) <=> (creative(X0) | ~generous(X0))) [input p12]
16. ! [X0] : ((patient(X0) <~> ~old(X0)) => (~old(X0) <~> ~humble(X0))) [input p15]
22. ~quiet(susan) | ~patient(susan) [input p21]
25. calm(susan) [input hypothesis]
32. ! [X0] : (~humble(X0) | ~quiet(X0)) [ennf transformation 8]
34. ! [X0] : ((~old(X0) <~> ~humble(X0)) | (patient(X0) <=> ~old(X0))) [ennf transformation 16]
35. ! [X0] : (((funny(X0) & ~quiet(X0)) | (generous(X0) | ~strong(X0))) & ((~generous(X0) & strong(X0)) | (~funny(X0) | quiet(X0)))) [nnf transformation 1]
36. ! [X0] : (((funny(X0) & ~quiet(X0)) | generous(X0) | ~strong(X0)) & ((~generous(X0) & strong(X0)) | ~funny(X0) | quiet(X0))) [flattening 35]
39. ! [X0] : (((calm(X0) | ~generous(X0)) | (~funny(X0) | ~calm(X0))) & ((funny(X0) & calm(X0)) | (~calm(X0) & generous(X0)))) [nnf transformation 5]
40. ! [X0] : ((calm(X0) | ~generous(X0) | ~funny(X0) | ~calm(X0)) & ((funny(X0) & calm(X0)) | (~calm(X0) & generous(X0)))) [flattening 39]
46. ! [X0] : (((~strong(X0) & ~funny(X0)) | ((~old(X0) | creative(X0)) & (~creative(X0) | old(X0)))) & (((creative(X0) | old(X0)) & (~creative(X0) | ~old(X0))) | (strong(X0) | funny(X0)))) [nnf transformation 9]
47. ! [X0] : (((~strong(X0) & ~funny(X0)) | ((~old(X0) | creative(X0)) & (~creative(X0) | old(X0)))) & (((creative(X0) | old(X0)) & (~creative(X0) | ~old(X0))) | strong(X0) | funny(X0))) [flattening 46]
57. ! [X0] : (((~calm(X0) & wise(X0)) | (~creative(X0) & generous(X0))) & ((creative(X0) | ~generous(X0)) | (calm(X0) | ~wise(X0)))) [nnf transformation 13]
58. ! [X0] : (((~calm(X0) & wise(X0)) | (~creative(X0) & generous(X0))) & (creative(X0) | ~generous(X0) | calm(X0) | ~wise(X0))) [flattening 57]
66. ! [X0] : (((humble(X0) | old(X0)) & (~humble(X0) | ~old(X0))) | ((patient(X0) | old(X0)) & (~old(X0) | ~patient(X0)))) [nnf transformation 34]
76. ~generous(X0) | ~funny(X0) | quiet(X0) [cnf transformation 36]
87. calm(X0) | generous(X0) [cnf transformation 40]
90. ~calm(X0) | funny(X0) [cnf transformation 40]
102. ~humble(X0) | ~quiet(X0) [cnf transformation 32]
106. ~old(X0) | ~funny(X0) | creative(X0) [cnf transformation 47]
124. ~calm(X0) | generous(X0) [cnf transformation 58]
125. ~creative(X0) | ~calm(X0) [cnf transformation 58]
137. humble(X0) | old(X0) | patient(X0) | old(X0) [cnf transformation 66]
145. ~quiet(susan) | ~patient(susan) [cnf transformation 22]
149. calm(susan) [cnf transformation 25]
151. old(X0) | humble(X0) | patient(X0) [duplicate literal removal 137]
237. generous(X0) [subsumption resolution 124,87]
314. 33 <=> patient(susan) [avatar definition]
316. ~patient(susan) <- (~33) [avatar component clause 314]
318. 34 <=> quiet(susan) [avatar definition]
319. quiet(susan) <- (34) [avatar component clause 318]
321. ~33 | ~34 [avatar split clause 145,318,314]
325. funny(susan) [resolution 90,149]
347. ~funny(X1) | quiet(X1) [resolution 76,237]
348. quiet(susan) [resolution 347,325]
349. 34 [avatar split clause 348,318]
356. ~funny(X2) | patient(X2) | humble(X2) | creative(X2) [resolution 151,106]
420. 42 <=> creative(susan) [avatar definition]
421. ~creative(susan) <- (~42) [avatar component clause 420]
422. creative(susan) <- (42) [avatar component clause 420]
424. 43 <=> humble(susan) [avatar definition]
426. humble(susan) <- (43) [avatar component clause 424]
442. ~calm(susan) <- (42) [resolution 422,125]
445. $false <- (42) [subsumption resolution 442,149]
446. ~42 [avatar contradiction clause 445]
447. patient(susan) | humble(susan) | creative(susan) [resolution 356,325]
459. ~quiet(susan) <- (43) [resolution 426,102]
460. $false <- (34, 43) [subsumption resolution 459,319]
461. ~34 | ~43 [avatar contradiction clause 460]
472. humble(susan) | creative(susan) <- (~33) [subsumption resolution 447,316]
473. humble(susan) <- (~33, ~42) [subsumption resolution 472,421]
474. 43 | 33 | 42 [avatar split clause 473,420,314,424]
475. $false [avatar sat refutation 321,349,446,461,474]
% SZS output end Proof for 798665042790823080872911
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If paul is either not humble or generous then someone is both patient and tall. If alice is either not happy or calm then someone is not wise or not quiet and vice versa. Everyone who is either not funny or wise is both happy and quiet and vice versa. Everyone who is old is not kind or creative. If someone is not patient or calm then alice is not generous and vice versa. Everyone who is either not wise or not strong is happy. If john is curious then someone is either brave or not brave and vice versa. If alice is both not rich and not brave then alice is both not patient and quiet. Everyone who is both happy and kind is not generous and vice versa. Everyone who is old or not patient is both funny and tall and vice versa. Everyone who is either generous or not humble is quiet and vice versa. Everyone who is either not rich or not calm is not rich or not humble. If susan is not brave or tall then someone is not curious and vice versa. Everyone who is either not creative or not brave is not humble. Everyone who is not happy is patient or not quiet. Everyone who is both not humble and not brave is both not curious and not generous. Alice is strong or quiet. Someone is brave. John is both generous and not calm. Alice is humble or old. Someone is both humble and rich. John is both quiet and wise. Mary is both not rich and not old. Someone is either brave or not happy. | Alice is kind. | entailment | (((~humble(paul)<~>generous(paul)))=>(?[X]:((patient(X)&tall(X)))))&
(((~happy(alice)<~>calm(alice)))<=>(?[X]:((~wise(X)|~quiet(X)))))&
(![X]:((~funny(X)<~>wise(X))<=>(happy(X)&quiet(X))))&
(![X]:(old(X)=>(~kind(X)|creative(X))))&
((?[X]:((~patient(X)|calm(X))))<=>(~generous(alice)))&
(![X]:((~wise(X)<~>~strong(X))=>happy(X)))&
((curious(john))<=>(?[X]:((brave(X)<~>~brave(X)))))&
(((~rich(alice)&~brave(alice)))=>((~patient(alice)&quiet(alice))))&
(![X]:((happy(X)&kind(X))<=>~generous(X)))&
(![X]:((old(X)|~patient(X))<=>(funny(X)&tall(X))))&
(![X]:((generous(X)<~>~humble(X))<=>quiet(X)))&
(![X]:((~rich(X)<~>~calm(X))=>(~rich(X)|~humble(X))))&
(((~brave(susan)|tall(susan)))<=>(?[X]:(~curious(X))))&
(![X]:((~creative(X)<~>~brave(X))=>~humble(X)))&
(![X]:(~happy(X)=>(patient(X)|~quiet(X))))&
(![X]:((~humble(X)&~brave(X))=>(~curious(X)&~generous(X))))&
((strong(alice)|quiet(alice)))&
(?[X]:(brave(X)))&
((generous(john)&~calm(john)))&
((humble(alice)|old(alice)))&
(?[X]:((humble(X)&rich(X))))&
((quiet(john)&wise(john)))&
((~rich(mary)&~old(mary)))&
(?[X]:((brave(X)<~>~happy(X)))) | kind(alice) | [
"p4",
"p8",
"p11",
"p20",
"hypothesis"
] | % SZS status Unsatisfiable for 5539512191839124832209510
% SZS output start Proof for 5539512191839124832209510
5. ? [X0] : (calm(X0) | ~patient(X0)) <=> ~generous(alice) [input p4]
9. ! [X0] : ((kind(X0) & happy(X0)) <=> ~generous(X0)) [input p8]
12. ! [X0] : ((~rich(X0) <~> ~calm(X0)) => (~humble(X0) | ~rich(X0))) [input p11]
21. ? [X0] : (rich(X0) & humble(X0)) [input p20]
25. ~kind(alice) [input hypothesis]
32. ! [X0] : ((~humble(X0) | ~rich(X0)) | (~rich(X0) <=> ~calm(X0))) [ennf transformation 12]
33. ! [X0] : (~humble(X0) | ~rich(X0) | (~rich(X0) <=> ~calm(X0))) [flattening 32]
48. (? [X0] : (calm(X0) | ~patient(X0)) | generous(alice)) & (~generous(alice) | ! [X0] : (~calm(X0) & patient(X0))) [nnf transformation 5]
49. (? [X0] : (calm(X0) | ~patient(X0)) | generous(alice)) & (~generous(alice) | ! [X1] : (~calm(X1) & patient(X1))) [rectify 48]
50. ? [X0] : (calm(X0) | ~patient(X0)) => (calm(sK2) | ~patient(sK2)) [choice axiom]
51. ((calm(sK2) | ~patient(sK2)) | generous(alice)) & (~generous(alice) | ! [X1] : (~calm(X1) & patient(X1))) [skolemisation 49,50]
57. ! [X0] : (((kind(X0) & happy(X0)) | generous(X0)) & (~generous(X0) | (~kind(X0) | ~happy(X0)))) [nnf transformation 9]
58. ! [X0] : (((kind(X0) & happy(X0)) | generous(X0)) & (~generous(X0) | ~kind(X0) | ~happy(X0))) [flattening 57]
62. ! [X0] : (~humble(X0) | ~rich(X0) | ((~rich(X0) | calm(X0)) & (~calm(X0) | rich(X0)))) [nnf transformation 33]
71. ? [X0] : (rich(X0) & humble(X0)) => (rich(sK6) & humble(sK6)) [choice axiom]
72. rich(sK6) & humble(sK6) [skolemisation 21,71]
94. ~generous(alice) | ~calm(X1) [cnf transformation 51]
106. kind(X0) | generous(X0) [cnf transformation 58]
117. ~humble(X0) | ~rich(X0) | ~rich(X0) | calm(X0) [cnf transformation 62]
131. humble(sK6) [cnf transformation 72]
132. rich(sK6) [cnf transformation 72]
139. ~kind(alice) [cnf transformation 25]
140. ~rich(X0) | ~humble(X0) | calm(X0) [duplicate literal removal 117]
192. 11 <=> generous(alice) [avatar definition]
205. 14 <=> ! [X1] : ~calm(X1) [avatar definition]
206. ~calm(X1) <- (14) [avatar component clause 205]
207. 14 | ~11 [avatar split clause 94,192,205]
288. generous(alice) [resolution 106,139]
291. 11 [avatar split clause 288,192]
362. ~humble(sK6) | calm(sK6) [resolution 140,132]
364. calm(sK6) [subsumption resolution 362,131]
365. $false <- (14) [subsumption resolution 364,206]
366. ~14 [avatar contradiction clause 365]
370. $false [avatar sat refutation 207,291,366]
% SZS output end Proof for 5539512191839124832209510
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both funny and not quiet then someone is not funny or quiet.
Everyone who is either not humble or not rich is calm and vice versa.
Everyone who is either humble or calm is either strong or rich.
Everyone who is not happy is either not happy or not humble and vice versa.
Everyone who is both not humble and kind is both not humble and quiet and vice versa.
If fred is either humble or curious then someone is both not humble and not calm.
Everyone who is rich or not generous is old or not rich and vice versa.
Everyone who is not wise is curious.
Everyone who is both old and creative is both not rich and not old and vice versa.
If lucy is either not generous or generous then mary is both humble and not patient and vice versa.
Everyone who is wise is not curious and vice versa.
Everyone who is old is either not tall or strong.
Everyone who is not rich or not old is creative or not old.
If mary is funny or not kind then john is not funny or humble and vice versa.
If someone is rich then someone is old and vice versa.
Everyone who is both not quiet and rich is strong and vice versa.
John is both rich and curious.
John is either brave or creative.
Someone is not funny.
Someone is not creative.
Someone is wise.
Paul is happy or not calm.
Paul is generous. | Lucy is curious. | neutral | ((?[X]:((funny(X)&~quiet(X))))=>(?[X]:((~funny(X)|quiet(X)))))&
(![X]:((~humble(X)<~>~rich(X))<=>calm(X)))&
(![X]:((humble(X)<~>calm(X))=>(strong(X)<~>rich(X))))&
(![X]:(~happy(X)<=>(~happy(X)<~>~humble(X))))&
(![X]:((~humble(X)&kind(X))<=>(~humble(X)&quiet(X))))&
(((humble(fred)<~>curious(fred)))=>(?[X]:((~humble(X)&~calm(X)))))&
(![X]:((rich(X)|~generous(X))<=>(old(X)|~rich(X))))&
(![X]:(~wise(X)=>curious(X)))&
(![X]:((old(X)&creative(X))<=>(~rich(X)&~old(X))))&
(((~generous(lucy)<~>generous(lucy)))<=>((humble(mary)&~patient(mary))))&
(![X]:(wise(X)<=>~curious(X)))&
(![X]:(old(X)=>(~tall(X)<~>strong(X))))&
(![X]:((~rich(X)|~old(X))=>(creative(X)|~old(X))))&
(((funny(mary)|~kind(mary)))<=>((~funny(john)|humble(john))))&
((?[X]:(rich(X)))<=>(?[X]:(old(X))))&
(![X]:((~quiet(X)&rich(X))<=>strong(X)))&
((rich(john)&curious(john)))&
((brave(john)<~>creative(john)))&
(?[X]:(~funny(X)))&
(?[X]:(~creative(X)))&
(?[X]:(wise(X)))&
((happy(paul)|~calm(paul)))&
(generous(paul)) | curious(lucy) | [] | null | 0 |
Everyone who is either not wise or quiet is either curious or not curious and vice versa. If someone is both not tall and rich then lucy is not tall or not quiet. Everyone who is patient is not brave or patient and vice versa. Everyone who is tall or funny is not humble and vice versa. If someone is both not old and not strong then lucy is not funny and vice versa. Everyone who is either not happy or not wise is not calm or not happy. If someone is not curious then someone is not generous or tall. Everyone who is either not old or not wise is happy or brave. If john is rich or curious then john is both quiet and brave and vice versa. Everyone who is not strong is not humble. Everyone who is wise or not quiet is either not humble or not generous and vice versa. Everyone who is happy is not wise or happy. If someone is both not calm and quiet then paul is both not wise and not funny and vice versa. If someone is either not patient or tall then susan is both not patient and old. If fred is not creative or curious then fred is both generous and not tall. If john is not old or not quiet then susan is not brave or not generous and vice versa. Someone is either brave or not creative. Someone is patient. Lucy is not generous or not humble. Someone is both curious and not calm. Someone is rich. Someone is not wise or not happy. Susan is not generous. John is not humble or not tall. | Paul is not brave. | neutral | (![X]:((~wise(X)<~>quiet(X))<=>(curious(X)<~>~curious(X))))&
((?[X]:((~tall(X)&rich(X))))=>((~tall(lucy)|~quiet(lucy))))&
(![X]:(patient(X)<=>(~brave(X)|patient(X))))&
(![X]:((tall(X)|funny(X))<=>~humble(X)))&
((?[X]:((~old(X)&~strong(X))))<=>(~funny(lucy)))&
(![X]:((~happy(X)<~>~wise(X))=>(~calm(X)|~happy(X))))&
((?[X]:(~curious(X)))=>(?[X]:((~generous(X)|tall(X)))))&
(![X]:((~old(X)<~>~wise(X))=>(happy(X)|brave(X))))&
(((rich(john)|curious(john)))<=>((quiet(john)&brave(john))))&
(![X]:(~strong(X)=>~humble(X)))&
(![X]:((wise(X)|~quiet(X))<=>(~humble(X)<~>~generous(X))))&
(![X]:(happy(X)=>(~wise(X)|happy(X))))&
((?[X]:((~calm(X)&quiet(X))))<=>((~wise(paul)&~funny(paul))))&
((?[X]:((~patient(X)<~>tall(X))))=>((~patient(susan)&old(susan))))&
(((~creative(fred)|curious(fred)))=>((generous(fred)&~tall(fred))))&
(((~old(john)|~quiet(john)))<=>((~brave(susan)|~generous(susan))))&
(?[X]:((brave(X)<~>~creative(X))))&
(?[X]:(patient(X)))&
((~generous(lucy)|~humble(lucy)))&
(?[X]:((curious(X)&~calm(X))))&
(?[X]:(rich(X)))&
(?[X]:((~wise(X)|~happy(X))))&
(~generous(susan))&
((~humble(john)|~tall(john))) | ~brave(paul) | [] | null | 0 |
Everyone who is calm is both not humble and generous.
Everyone who is not brave or tall is either not brave or calm.
If someone is not tall or wise then lucy is both curious and not curious and vice versa.
Everyone who is either not old or calm is both not curious and humble and vice versa.
If paul is creative or not kind then someone is either rich or not tall and vice versa.
Everyone who is patient is both not funny and not quiet and vice versa.
Everyone who is humble is wise or tall and vice versa.
Everyone who is both curious and not kind is either not creative or not tall and vice versa.
Everyone who is both brave and not strong is either happy or generous and vice versa.
Everyone who is funny or humble is either humble or not kind.
If susan is either not happy or not strong then susan is old or curious.
If paul is either quiet or patient then fred is either not strong or not creative and vice versa.
Everyone who is not happy or not brave is not wise and vice versa.
Everyone who is both not calm and wise is either brave or curious.
If susan is both not humble and kind then paul is both kind and not patient and vice versa.
Everyone who is wise is either not creative or calm and vice versa.
Alice is not calm or not quiet.
Someone is both not generous and funny.
Someone is not old or wise.
Someone is strong.
Someone is either strong or not tall. | Alice is happy. | neutral | (![X]:(calm(X)=>(~humble(X)&generous(X))))&
(![X]:((~brave(X)|tall(X))=>(~brave(X)<~>calm(X))))&
((?[X]:((~tall(X)|wise(X))))<=>((curious(lucy)&~curious(lucy))))&
(![X]:((~old(X)<~>calm(X))<=>(~curious(X)&humble(X))))&
(((creative(paul)|~kind(paul)))<=>(?[X]:((rich(X)<~>~tall(X)))))&
(![X]:(patient(X)<=>(~funny(X)&~quiet(X))))&
(![X]:(humble(X)<=>(wise(X)|tall(X))))&
(![X]:((curious(X)&~kind(X))<=>(~creative(X)<~>~tall(X))))&
(![X]:((brave(X)&~strong(X))<=>(happy(X)<~>generous(X))))&
(![X]:((funny(X)|humble(X))=>(humble(X)<~>~kind(X))))&
(((~happy(susan)<~>~strong(susan)))=>((old(susan)|curious(susan))))&
(((quiet(paul)<~>patient(paul)))<=>((~strong(fred)<~>~creative(fred))))&
(![X]:((~happy(X)|~brave(X))<=>~wise(X)))&
(![X]:((~calm(X)&wise(X))=>(brave(X)<~>curious(X))))&
(((~humble(susan)&kind(susan)))<=>((kind(paul)&~patient(paul))))&
(![X]:(wise(X)<=>(~creative(X)<~>calm(X))))&
((~calm(alice)|~quiet(alice)))&
(?[X]:((~generous(X)&funny(X))))&
(?[X]:((~old(X)|wise(X))))&
(?[X]:(strong(X)))&
(?[X]:((strong(X)<~>~tall(X)))) | happy(alice) | [] | null | 0 |
If john is funny or quiet then someone is not strong or not quiet.
If someone is patient then mary is not quiet or not kind.
Everyone who is curious is either curious or not humble.
If someone is both not tall and not kind then someone is both strong and generous.
Everyone who is not brave or not curious is tall or not old.
Everyone who is either not old or quiet is either quiet or not rich and vice versa.
If someone is funny or not calm then fred is either not curious or not calm and vice versa.
Everyone who is not calm or not strong is both humble and not creative.
If someone is both creative and not creative then someone is either not curious or quiet.
Everyone who is not patient or not old is both not brave and patient and vice versa.
Everyone who is quiet or not brave is both not old and wise.
Everyone who is both strong and not calm is not funny or funny and vice versa.
If someone is either not funny or not creative then fred is not wise or not creative and vice versa.
If john is either funny or humble then susan is not generous or quiet and vice versa.
Everyone who is not humble is both not patient and humble and vice versa.
Someone is both not creative and patient.
Someone is either quiet or not quiet.
Fred is either strong or not funny.
Paul is either tall or brave.
Someone is either quiet or not funny.
Susan is funny or curious.
Lucy is strong. | Fred is not quiet. | neutral | (((funny(john)|quiet(john)))=>(?[X]:((~strong(X)|~quiet(X)))))&
((?[X]:(patient(X)))=>((~quiet(mary)|~kind(mary))))&
(![X]:(curious(X)=>(curious(X)<~>~humble(X))))&
((?[X]:((~tall(X)&~kind(X))))=>(?[X]:((strong(X)&generous(X)))))&
(![X]:((~brave(X)|~curious(X))=>(tall(X)|~old(X))))&
(![X]:((~old(X)<~>quiet(X))<=>(quiet(X)<~>~rich(X))))&
((?[X]:((funny(X)|~calm(X))))<=>((~curious(fred)<~>~calm(fred))))&
(![X]:((~calm(X)|~strong(X))=>(humble(X)&~creative(X))))&
((?[X]:((creative(X)&~creative(X))))=>(?[X]:((~curious(X)<~>quiet(X)))))&
(![X]:((~patient(X)|~old(X))<=>(~brave(X)&patient(X))))&
(![X]:((quiet(X)|~brave(X))=>(~old(X)&wise(X))))&
(![X]:((strong(X)&~calm(X))<=>(~funny(X)|funny(X))))&
((?[X]:((~funny(X)<~>~creative(X))))<=>((~wise(fred)|~creative(fred))))&
(((funny(john)<~>humble(john)))<=>((~generous(susan)|quiet(susan))))&
(![X]:(~humble(X)<=>(~patient(X)&humble(X))))&
(?[X]:((~creative(X)&patient(X))))&
(?[X]:((quiet(X)<~>~quiet(X))))&
((strong(fred)<~>~funny(fred)))&
((tall(paul)<~>brave(paul)))&
(?[X]:((quiet(X)<~>~funny(X))))&
((funny(susan)|curious(susan)))&
(strong(lucy)) | ~quiet(fred) | [] | null | 0 |
Everyone who is both happy and not wise is either creative or curious and vice versa.
Everyone who is humble or not old is creative or not kind.
Everyone who is not funny or brave is not tall or not rich.
If someone is rich then susan is either calm or not curious and vice versa.
Everyone who is not rich or tall is either not brave or not patient.
Everyone who is not creative is both not strong and not quiet.
If someone is both not brave and patient then fred is not strong or not quiet and vice versa.
If susan is both patient and curious then fred is not strong or humble.
Everyone who is patient or not tall is either quiet or rich and vice versa.
If paul is both not curious and not tall then alice is not rich or not creative and vice versa.
Everyone who is either not calm or not old is quiet and vice versa.
Everyone who is not old or calm is not happy or not curious and vice versa.
Everyone who is not tall or wise is tall.
If someone is not humble then john is curious and vice versa.
If paul is both not tall and not happy then mary is not rich or not strong and vice versa.
If fred is both not rich and generous then someone is curious or patient and vice versa.
Someone is either old or not calm.
Someone is not old or old.
Mary is either happy or not generous.
Someone is not strong or kind.
Paul is not humble.
Someone is both not quiet and not old.
Someone is creative or happy. | Susan is patient. | neutral | (![X]:((happy(X)&~wise(X))<=>(creative(X)<~>curious(X))))&
(![X]:((humble(X)|~old(X))=>(creative(X)|~kind(X))))&
(![X]:((~funny(X)|brave(X))=>(~tall(X)|~rich(X))))&
((?[X]:(rich(X)))<=>((calm(susan)<~>~curious(susan))))&
(![X]:((~rich(X)|tall(X))=>(~brave(X)<~>~patient(X))))&
(![X]:(~creative(X)=>(~strong(X)&~quiet(X))))&
((?[X]:((~brave(X)&patient(X))))<=>((~strong(fred)|~quiet(fred))))&
(((patient(susan)&curious(susan)))=>((~strong(fred)|humble(fred))))&
(![X]:((patient(X)|~tall(X))<=>(quiet(X)<~>rich(X))))&
(((~curious(paul)&~tall(paul)))<=>((~rich(alice)|~creative(alice))))&
(![X]:((~calm(X)<~>~old(X))<=>quiet(X)))&
(![X]:((~old(X)|calm(X))<=>(~happy(X)|~curious(X))))&
(![X]:((~tall(X)|wise(X))=>tall(X)))&
((?[X]:(~humble(X)))<=>(curious(john)))&
(((~tall(paul)&~happy(paul)))<=>((~rich(mary)|~strong(mary))))&
(((~rich(fred)&generous(fred)))<=>(?[X]:((curious(X)|patient(X)))))&
(?[X]:((old(X)<~>~calm(X))))&
(?[X]:((~old(X)|old(X))))&
((happy(mary)<~>~generous(mary)))&
(?[X]:((~strong(X)|kind(X))))&
(~humble(paul))&
(?[X]:((~quiet(X)&~old(X))))&
(?[X]:((creative(X)|happy(X)))) | patient(susan) | [] | null | 0 |
If mary is both not wise and rich then susan is generous and vice versa.
Everyone who is both not kind and wise is not wise and vice versa.
Everyone who is either not strong or not kind is both not brave and brave.
Everyone who is either wise or strong is either rich or humble and vice versa.
Everyone who is both not kind and not old is not patient and vice versa.
If fred is not strong or calm then john is not curious or rich and vice versa.
If susan is either strong or old then john is patient and vice versa.
Everyone who is both generous and not calm is funny or tall.
Everyone who is both calm and strong is not patient and vice versa.
If someone is tall then fred is generous or brave.
Everyone who is either not wise or not brave is either not wise or not generous and vice versa.
If someone is quiet then someone is not strong or generous.
If someone is not generous or not funny then someone is either humble or brave and vice versa.
Everyone who is not tall is curious or not old.
If someone is both not old and curious then someone is either not funny or generous.
Someone is old or brave.
Mary is either humble or not humble.
Someone is funny.
Someone is tall.
Someone is wise or not funny.
Someone is quiet.
Susan is either not tall or creative. | Susan is patient. | entailment | (((~wise(mary)&rich(mary)))<=>(generous(susan)))&
(![X]:((~kind(X)&wise(X))<=>~wise(X)))&
(![X]:((~strong(X)<~>~kind(X))=>(~brave(X)&brave(X))))&
(![X]:((wise(X)<~>strong(X))<=>(rich(X)<~>humble(X))))&
(![X]:((~kind(X)&~old(X))<=>~patient(X)))&
(((~strong(fred)|calm(fred)))<=>((~curious(john)|rich(john))))&
(((strong(susan)<~>old(susan)))<=>(patient(john)))&
(![X]:((generous(X)&~calm(X))=>(funny(X)|tall(X))))&
(![X]:((calm(X)&strong(X))<=>~patient(X)))&
((?[X]:(tall(X)))=>((generous(fred)|brave(fred))))&
(![X]:((~wise(X)<~>~brave(X))<=>(~wise(X)<~>~generous(X))))&
((?[X]:(quiet(X)))=>(?[X]:((~strong(X)|generous(X)))))&
((?[X]:((~generous(X)|~funny(X))))<=>(?[X]:((humble(X)<~>brave(X)))))&
(![X]:(~tall(X)=>(curious(X)|~old(X))))&
((?[X]:((~old(X)&curious(X))))=>(?[X]:((~funny(X)<~>generous(X)))))&
(?[X]:((old(X)|brave(X))))&
((humble(mary)<~>~humble(mary)))&
(?[X]:(funny(X)))&
(?[X]:(tall(X)))&
(?[X]:((wise(X)|~funny(X))))&
(?[X]:(quiet(X)))&
((~tall(susan)<~>creative(susan))) | patient(susan) | [
"p1",
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 3303071319862922389614672
% SZS output start Proof for 3303071319862922389614672
2. ! [X0] : ((wise(X0) & ~kind(X0)) <=> ~wise(X0)) [input p1]
5. ! [X0] : ((~old(X0) & ~kind(X0)) <=> ~patient(X0)) [input p4]
23. ~patient(susan) [input hypothesis]
38. ! [X0] : (((wise(X0) & ~kind(X0)) | wise(X0)) & (~wise(X0) | (~wise(X0) | kind(X0)))) [nnf transformation 2]
39. ! [X0] : (((wise(X0) & ~kind(X0)) | wise(X0)) & (~wise(X0) | ~wise(X0) | kind(X0))) [flattening 38]
42. ! [X0] : (((~old(X0) & ~kind(X0)) | patient(X0)) & (~patient(X0) | (old(X0) | kind(X0)))) [nnf transformation 5]
43. ! [X0] : (((~old(X0) & ~kind(X0)) | patient(X0)) & (~patient(X0) | old(X0) | kind(X0))) [flattening 42]
77. ~wise(X0) | ~wise(X0) | kind(X0) [cnf transformation 39]
79. wise(X0) | wise(X0) [cnf transformation 39]
93. ~kind(X0) | patient(X0) [cnf transformation 43]
135. ~patient(susan) [cnf transformation 23]
140. ~wise(X0) | kind(X0) [duplicate literal removal 77]
141. wise(X0) [duplicate literal removal 79]
157. kind(X0) [subsumption resolution 140,141]
165. patient(X0) [subsumption resolution 93,157]
276. $false [subsumption resolution 135,165]
% SZS output end Proof for 3303071319862922389614672
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.035 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not curious or wise is either not funny or kind and vice versa.
Everyone who is both not rich and strong is not old or creative and vice versa.
Everyone who is either not wise or strong is both not quiet and not happy.
Everyone who is calm is either not wise or not humble.
Everyone who is either curious or brave is both not kind and rich and vice versa.
Everyone who is kind or not funny is both not strong and happy.
Everyone who is not curious is either not generous or not patient.
Everyone who is either not funny or quiet is humble or not creative and vice versa.
Everyone who is not funny or not calm is both kind and not strong.
Everyone who is either not brave or happy is either not brave or curious.
If someone is both rich and not humble then mary is both wise and not funny and vice versa.
Everyone who is creative or funny is both happy and not humble and vice versa.
If someone is both brave and humble then fred is not rich and vice versa.
If someone is not tall then john is not funny and vice versa.
If lucy is curious or kind then mary is not brave and vice versa.
Someone is happy or rich.
Someone is generous.
Susan is kind or not kind.
Someone is not quiet or not patient.
Someone is rich or calm. | John is wise. | entailment | (![X]:((~curious(X)<~>wise(X))<=>(~funny(X)<~>kind(X))))&
(![X]:((~rich(X)&strong(X))<=>(~old(X)|creative(X))))&
(![X]:((~wise(X)<~>strong(X))=>(~quiet(X)&~happy(X))))&
(![X]:(calm(X)=>(~wise(X)<~>~humble(X))))&
(![X]:((curious(X)<~>brave(X))<=>(~kind(X)&rich(X))))&
(![X]:((kind(X)|~funny(X))=>(~strong(X)&happy(X))))&
(![X]:(~curious(X)=>(~generous(X)<~>~patient(X))))&
(![X]:((~funny(X)<~>quiet(X))<=>(humble(X)|~creative(X))))&
(![X]:((~funny(X)|~calm(X))=>(kind(X)&~strong(X))))&
(![X]:((~brave(X)<~>happy(X))=>(~brave(X)<~>curious(X))))&
((?[X]:((rich(X)&~humble(X))))<=>((wise(mary)&~funny(mary))))&
(![X]:((creative(X)|funny(X))<=>(happy(X)&~humble(X))))&
((?[X]:((brave(X)&humble(X))))<=>(~rich(fred)))&
((?[X]:(~tall(X)))<=>(~funny(john)))&
(((curious(lucy)|kind(lucy)))<=>(~brave(mary)))&
(?[X]:((happy(X)|rich(X))))&
(?[X]:(generous(X)))&
((kind(susan)|~kind(susan)))&
(?[X]:((~quiet(X)|~patient(X))))&
(?[X]:((rich(X)|calm(X)))) | wise(john) | [
"p2",
"p3",
"p5",
"p8",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 3387026445501505903376051
% SZS output start Proof for 3387026445501505903376051
3. ! [X0] : ((~wise(X0) <~> strong(X0)) => (~happy(X0) & ~quiet(X0))) [input p2]
4. ! [X0] : (calm(X0) => (~wise(X0) <~> ~humble(X0))) [input p3]
6. ! [X0] : ((~funny(X0) | kind(X0)) => (happy(X0) & ~strong(X0))) [input p5]
9. ! [X0] : ((~calm(X0) | ~funny(X0)) => (~strong(X0) & kind(X0))) [input p8]
12. ! [X0] : ((funny(X0) | creative(X0)) <=> (~humble(X0) & happy(X0))) [input p11]
21. ~wise(john) [input hypothesis]
22. ! [X0] : ((~happy(X0) & ~quiet(X0)) | (~wise(X0) <=> strong(X0))) [ennf transformation 3]
23. ! [X0] : ((~wise(X0) <~> ~humble(X0)) | ~calm(X0)) [ennf transformation 4]
24. ! [X0] : ((happy(X0) & ~strong(X0)) | (funny(X0) & ~kind(X0))) [ennf transformation 6]
26. ! [X0] : ((~strong(X0) & kind(X0)) | (calm(X0) & funny(X0))) [ennf transformation 9]
31. ! [X0] : ((~happy(X0) & ~quiet(X0)) | ((~wise(X0) | ~strong(X0)) & (strong(X0) | wise(X0)))) [nnf transformation 22]
32. ! [X0] : (((humble(X0) | wise(X0)) & (~humble(X0) | ~wise(X0))) | ~calm(X0)) [nnf transformation 23]
44. ! [X0] : (((funny(X0) | creative(X0)) | (humble(X0) | ~happy(X0))) & ((~humble(X0) & happy(X0)) | (~funny(X0) & ~creative(X0)))) [nnf transformation 12]
45. ! [X0] : ((funny(X0) | creative(X0) | humble(X0) | ~happy(X0)) & ((~humble(X0) & happy(X0)) | (~funny(X0) & ~creative(X0)))) [flattening 44]
79. ~happy(X0) | strong(X0) | wise(X0) [cnf transformation 31]
82. ~calm(X0) | wise(X0) | humble(X0) [cnf transformation 32]
89. ~strong(X0) | ~kind(X0) [cnf transformation 24]
90. ~strong(X0) | funny(X0) [cnf transformation 24]
92. happy(X0) | funny(X0) [cnf transformation 24]
102. calm(X0) | kind(X0) [cnf transformation 26]
114. happy(X0) | ~funny(X0) [cnf transformation 45]
116. ~humble(X0) | ~funny(X0) [cnf transformation 45]
131. ~wise(john) [cnf transformation 21]
158. happy(X0) [subsumption resolution 114,92]
231. strong(X0) | wise(X0) | funny(X0) [resolution 79,92]
232. strong(X1) | wise(X1) [resolution 79,158]
233. funny(X0) | wise(X0) [subsumption resolution 231,90]
236. wise(X2) | ~kind(X2) [resolution 232,89]
252. wise(X0) | humble(X0) | kind(X0) [resolution 82,102]
253. humble(X0) | wise(X0) [subsumption resolution 252,236]
429. wise(X3) | ~funny(X3) [resolution 253,116]
432. wise(X3) [subsumption resolution 429,233]
437. $false [resolution 432,131]
% SZS output end Proof for 3387026445501505903376051
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is humble or not wise is quiet. Everyone who is either not happy or not calm is either not creative or not funny and vice versa. Everyone who is not wise or not happy is both curious and tall. If lucy is either patient or not patient then fred is either not curious or creative. If someone is humble then someone is both not tall and strong and vice versa. Everyone who is both not kind and not creative is either not patient or not funny and vice versa. Everyone who is either not happy or generous is both not quiet and brave. If paul is both not creative and quiet then john is strong or rich and vice versa. If susan is quiet then alice is not rich. Everyone who is both rich and not brave is not brave or not strong. Everyone who is kind is either brave or not brave and vice versa. Everyone who is humble is either not patient or kind and vice versa. Everyone who is curious or not generous is both not calm and strong and vice versa. Everyone who is not generous or not wise is both tall and not brave. Everyone who is not wise or humble is not curious and vice versa. If someone is both curious and tall then john is not patient or not tall and vice versa. Someone is either not curious or not happy. Someone is both creative and not patient. Alice is either calm or not patient. Someone is either patient or calm. | Fred is not tall. | neutral | (![X]:((humble(X)|~wise(X))=>quiet(X)))&
(![X]:((~happy(X)<~>~calm(X))<=>(~creative(X)<~>~funny(X))))&
(![X]:((~wise(X)|~happy(X))=>(curious(X)&tall(X))))&
(((patient(lucy)<~>~patient(lucy)))=>((~curious(fred)<~>creative(fred))))&
((?[X]:(humble(X)))<=>(?[X]:((~tall(X)&strong(X)))))&
(![X]:((~kind(X)&~creative(X))<=>(~patient(X)<~>~funny(X))))&
(![X]:((~happy(X)<~>generous(X))=>(~quiet(X)&brave(X))))&
(((~creative(paul)&quiet(paul)))<=>((strong(john)|rich(john))))&
((quiet(susan))=>(~rich(alice)))&
(![X]:((rich(X)&~brave(X))=>(~brave(X)|~strong(X))))&
(![X]:(kind(X)<=>(brave(X)<~>~brave(X))))&
(![X]:(humble(X)<=>(~patient(X)<~>kind(X))))&
(![X]:((curious(X)|~generous(X))<=>(~calm(X)&strong(X))))&
(![X]:((~generous(X)|~wise(X))=>(tall(X)&~brave(X))))&
(![X]:((~wise(X)|humble(X))<=>~curious(X)))&
((?[X]:((curious(X)&tall(X))))<=>((~patient(john)|~tall(john))))&
(?[X]:((~curious(X)<~>~happy(X))))&
(?[X]:((creative(X)&~patient(X))))&
((calm(alice)<~>~patient(alice)))&
(?[X]:((patient(X)<~>calm(X)))) | ~tall(fred) | [] | null | 0 |
Everyone who is either not kind or humble is either not calm or humble and vice versa.
If someone is either rich or not curious then susan is both calm and rich and vice versa.
Everyone who is either not strong or not brave is both patient and not calm.
Everyone who is calm or strong is either kind or not humble.
If someone is happy then someone is either happy or not generous.
Everyone who is both not humble and not patient is patient or not kind and vice versa.
If alice is both old and happy then someone is not patient or strong and vice versa.
Everyone who is both rich and patient is both strong and not patient.
Everyone who is both tall and not quiet is both not patient and patient and vice versa.
If mary is either not wise or old then mary is either not happy or rich.
If someone is humble or happy then mary is not brave.
Everyone who is not creative is both not kind and patient.
Everyone who is not rich is either not brave or creative and vice versa.
Everyone who is tall or quiet is creative or not humble and vice versa.
Everyone who is not calm or quiet is both not funny and happy.
Everyone who is generous or not kind is either not wise or not patient.
Someone is not rich or curious.
Someone is either kind or not kind.
Someone is wise.
Someone is either old or not kind.
Someone is both curious and creative.
John is tall.
Someone is either not quiet or not rich. | Susan is not happy. | contradiction | (![X]:((~kind(X)<~>humble(X))<=>(~calm(X)<~>humble(X))))&
((?[X]:((rich(X)<~>~curious(X))))<=>((calm(susan)&rich(susan))))&
(![X]:((~strong(X)<~>~brave(X))=>(patient(X)&~calm(X))))&
(![X]:((calm(X)|strong(X))=>(kind(X)<~>~humble(X))))&
((?[X]:(happy(X)))=>(?[X]:((happy(X)<~>~generous(X)))))&
(![X]:((~humble(X)&~patient(X))<=>(patient(X)|~kind(X))))&
(((old(alice)&happy(alice)))<=>(?[X]:((~patient(X)|strong(X)))))&
(![X]:((rich(X)&patient(X))=>(strong(X)&~patient(X))))&
(![X]:((tall(X)&~quiet(X))<=>(~patient(X)&patient(X))))&
(((~wise(mary)<~>old(mary)))=>((~happy(mary)<~>rich(mary))))&
((?[X]:((humble(X)|happy(X))))=>(~brave(mary)))&
(![X]:(~creative(X)=>(~kind(X)&patient(X))))&
(![X]:(~rich(X)<=>(~brave(X)<~>creative(X))))&
(![X]:((tall(X)|quiet(X))<=>(creative(X)|~humble(X))))&
(![X]:((~calm(X)|quiet(X))=>(~funny(X)&happy(X))))&
(![X]:((generous(X)|~kind(X))=>(~wise(X)<~>~patient(X))))&
(?[X]:((~rich(X)|curious(X))))&
(?[X]:((kind(X)<~>~kind(X))))&
(?[X]:(wise(X)))&
(?[X]:((old(X)<~>~kind(X))))&
(?[X]:((curious(X)&creative(X))))&
(tall(john))&
(?[X]:((~quiet(X)<~>~rich(X)))) | ~happy(susan) | [
"p5",
"p8",
"p11",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 6779313086027699945741549
% SZS output start Proof for 6779313086027699945741549
6. ! [X0] : ((~patient(X0) & ~humble(X0)) <=> (~kind(X0) | patient(X0))) [input p5]
9. ! [X0] : ((~quiet(X0) & tall(X0)) <=> (patient(X0) & ~patient(X0))) [input p8]
12. ! [X0] : (~creative(X0) => (patient(X0) & ~kind(X0))) [input p11]
14. ! [X0] : ((quiet(X0) | tall(X0)) <=> (~humble(X0) | creative(X0))) [input p13]
15. ! [X0] : ((quiet(X0) | ~calm(X0)) => (happy(X0) & ~funny(X0))) [input p14]
24. ~happy(susan) [input hypothesis]
26. ! [X0] : ((quiet(X0) | ~calm(X0)) => happy(X0)) [pure predicate removal 15]
34. ! [X0] : ((patient(X0) & ~kind(X0)) | creative(X0)) [ennf transformation 12]
35. ! [X0] : (happy(X0) | (~quiet(X0) & calm(X0))) [ennf transformation 26]
49. ! [X0] : (((~patient(X0) & ~humble(X0)) | (kind(X0) & ~patient(X0))) & ((~kind(X0) | patient(X0)) | (patient(X0) | humble(X0)))) [nnf transformation 6]
50. ! [X0] : (((~patient(X0) & ~humble(X0)) | (kind(X0) & ~patient(X0))) & (~kind(X0) | patient(X0) | patient(X0) | humble(X0))) [flattening 49]
56. ! [X0] : (((~quiet(X0) & tall(X0)) | (~patient(X0) | patient(X0))) & ((patient(X0) & ~patient(X0)) | (quiet(X0) | ~tall(X0)))) [nnf transformation 9]
57. ! [X0] : (((~quiet(X0) & tall(X0)) | ~patient(X0) | patient(X0)) & ((patient(X0) & ~patient(X0)) | quiet(X0) | ~tall(X0))) [flattening 56]
60. ! [X0] : (((quiet(X0) | tall(X0)) | (humble(X0) & ~creative(X0))) & ((~humble(X0) | creative(X0)) | (~quiet(X0) & ~tall(X0)))) [nnf transformation 14]
61. ! [X0] : ((quiet(X0) | tall(X0) | (humble(X0) & ~creative(X0))) & (~humble(X0) | creative(X0) | (~quiet(X0) & ~tall(X0)))) [flattening 60]
105. ~patient(X0) | ~patient(X0) [cnf transformation 50]
115. patient(X0) | quiet(X0) | ~tall(X0) [cnf transformation 57]
125. patient(X0) | creative(X0) [cnf transformation 34]
132. quiet(X0) | tall(X0) | ~creative(X0) [cnf transformation 61]
135. happy(X0) | ~quiet(X0) [cnf transformation 35]
151. ~happy(susan) [cnf transformation 24]
154. ~patient(X0) [duplicate literal removal 105]
221. quiet(X0) | ~tall(X0) [subsumption resolution 115,154]
251. creative(X0) [subsumption resolution 125,154]
255. quiet(X0) | tall(X0) [subsumption resolution 132,251]
256. quiet(X0) [subsumption resolution 255,221]
257. happy(X0) [subsumption resolution 135,256]
280. $false [subsumption resolution 151,257]
% SZS output end Proof for 6779313086027699945741549
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is calm is old or not creative and vice versa. If alice is either not wise or old then lucy is not humble or old and vice versa. Everyone who is both generous and not funny is not curious and vice versa. Everyone who is either not brave or not generous is wise or tall and vice versa. If someone is either not strong or not creative then someone is either old or not quiet and vice versa. Everyone who is both not rich and kind is not tall or rich and vice versa. Everyone who is not strong is generous or old and vice versa. Everyone who is curious is both not curious and not patient and vice versa. Everyone who is old is not kind or tall and vice versa. If someone is both rich and patient then fred is both not quiet and not brave. Everyone who is calm or brave is both not wise and brave and vice versa. If someone is either funny or not creative then someone is not curious and vice versa. If someone is both not generous and not tall then someone is not humble or not calm. Everyone who is curious or generous is either not happy or calm and vice versa. If someone is both tall and not wise then fred is both not wise and brave and vice versa. Someone is either not generous or not happy. Mary is old or kind. Someone is kind or not humble. Someone is not brave. Fred is not brave. Mary is patient or funny. | Lucy is kind. | entailment | (![X]:(calm(X)<=>(old(X)|~creative(X))))&
(((~wise(alice)<~>old(alice)))<=>((~humble(lucy)|old(lucy))))&
(![X]:((generous(X)&~funny(X))<=>~curious(X)))&
(![X]:((~brave(X)<~>~generous(X))<=>(wise(X)|tall(X))))&
((?[X]:((~strong(X)<~>~creative(X))))<=>(?[X]:((old(X)<~>~quiet(X)))))&
(![X]:((~rich(X)&kind(X))<=>(~tall(X)|rich(X))))&
(![X]:(~strong(X)<=>(generous(X)|old(X))))&
(![X]:(curious(X)<=>(~curious(X)&~patient(X))))&
(![X]:(old(X)<=>(~kind(X)|tall(X))))&
((?[X]:((rich(X)&patient(X))))=>((~quiet(fred)&~brave(fred))))&
(![X]:((calm(X)|brave(X))<=>(~wise(X)&brave(X))))&
((?[X]:((funny(X)<~>~creative(X))))<=>(?[X]:(~curious(X))))&
((?[X]:((~generous(X)&~tall(X))))=>(?[X]:((~humble(X)|~calm(X)))))&
(![X]:((curious(X)|generous(X))<=>(~happy(X)<~>calm(X))))&
((?[X]:((tall(X)&~wise(X))))<=>((~wise(fred)&brave(fred))))&
(?[X]:((~generous(X)<~>~happy(X))))&
((old(mary)|kind(mary)))&
(?[X]:((kind(X)|~humble(X))))&
(?[X]:(~brave(X)))&
(~brave(fred))&
((patient(mary)|funny(mary))) | kind(lucy) | [
"p0",
"p5",
"p8",
"p10",
"p14",
"p19",
"hypothesis"
] | % SZS status Unsatisfiable for 614545873428938748550888
% SZS output start Proof for 614545873428938748550888
1. ! [X0] : (calm(X0) <=> (~creative(X0) | old(X0))) [input p0]
6. ! [X0] : ((kind(X0) & ~rich(X0)) <=> (rich(X0) | ~tall(X0))) [input p5]
9. ! [X0] : (old(X0) <=> (tall(X0) | ~kind(X0))) [input p8]
11. ! [X0] : ((brave(X0) | calm(X0)) <=> (brave(X0) & ~wise(X0))) [input p10]
15. ? [X0] : (~wise(X0) & tall(X0)) <=> (brave(fred) & ~wise(fred)) [input p14]
20. ~brave(fred) [input p19]
22. ~kind(lucy) [input hypothesis]
28. ! [X0] : ((calm(X0) | (creative(X0) & ~old(X0))) & ((~creative(X0) | old(X0)) | ~calm(X0))) [nnf transformation 1]
29. ! [X0] : ((calm(X0) | (creative(X0) & ~old(X0))) & (~creative(X0) | old(X0) | ~calm(X0))) [flattening 28]
41. ! [X0] : (((kind(X0) & ~rich(X0)) | (~rich(X0) & tall(X0))) & ((rich(X0) | ~tall(X0)) | (~kind(X0) | rich(X0)))) [nnf transformation 6]
42. ! [X0] : (((kind(X0) & ~rich(X0)) | (~rich(X0) & tall(X0))) & (rich(X0) | ~tall(X0) | ~kind(X0) | rich(X0))) [flattening 41]
47. ! [X0] : ((old(X0) | (~tall(X0) & kind(X0))) & ((tall(X0) | ~kind(X0)) | ~old(X0))) [nnf transformation 9]
48. ! [X0] : ((old(X0) | (~tall(X0) & kind(X0))) & (tall(X0) | ~kind(X0) | ~old(X0))) [flattening 47]
49. ! [X0] : (((brave(X0) | calm(X0)) | (~brave(X0) | wise(X0))) & ((brave(X0) & ~wise(X0)) | (~brave(X0) & ~calm(X0)))) [nnf transformation 11]
50. ! [X0] : ((brave(X0) | calm(X0) | ~brave(X0) | wise(X0)) & ((brave(X0) & ~wise(X0)) | (~brave(X0) & ~calm(X0)))) [flattening 49]
61. (? [X0] : (~wise(X0) & tall(X0)) | (~brave(fred) | wise(fred))) & ((brave(fred) & ~wise(fred)) | ! [X0] : (wise(X0) | ~tall(X0))) [nnf transformation 15]
62. (? [X0] : (~wise(X0) & tall(X0)) | ~brave(fred) | wise(fred)) & ((brave(fred) & ~wise(fred)) | ! [X0] : (wise(X0) | ~tall(X0))) [flattening 61]
63. (? [X0] : (~wise(X0) & tall(X0)) | ~brave(fred) | wise(fred)) & ((brave(fred) & ~wise(fred)) | ! [X1] : (wise(X1) | ~tall(X1))) [rectify 62]
64. ? [X0] : (~wise(X0) & tall(X0)) => (~wise(sK5) & tall(sK5)) [choice axiom]
65. ((~wise(sK5) & tall(sK5)) | ~brave(fred) | wise(fred)) & ((brave(fred) & ~wise(fred)) | ! [X1] : (wise(X1) | ~tall(X1))) [skolemisation 63,64]
74. ~old(X0) | calm(X0) [cnf transformation 29]
102. kind(X0) | tall(X0) [cnf transformation 42]
111. kind(X0) | old(X0) [cnf transformation 48]
116. ~brave(X0) | ~wise(X0) [cnf transformation 50]
117. ~calm(X0) | brave(X0) [cnf transformation 50]
132. brave(fred) | wise(X1) | ~tall(X1) [cnf transformation 65]
140. ~brave(fred) [cnf transformation 20]
142. ~kind(lucy) [cnf transformation 22]
148. 1 <=> old(lucy) [avatar definition]
149. old(lucy) <- (1) [avatar component clause 148]
233. 18 <=> brave(fred) [avatar definition]
248. 21 <=> ! [X1] : (wise(X1) | ~tall(X1)) [avatar definition]
249. ~tall(X1) | wise(X1) <- (21) [avatar component clause 248]
250. 21 | 18 [avatar split clause 132,233,248]
275. ~18 [avatar split clause 140,233]
288. tall(lucy) [resolution 102,142]
293. old(lucy) [resolution 111,142]
294. 1 [avatar split clause 293,148]
295. calm(lucy) <- (1) [resolution 149,74]
298. brave(lucy) <- (1) [resolution 117,295]
303. ~wise(lucy) <- (1) [resolution 298,116]
306. wise(lucy) <- (21) [resolution 249,288]
307. $false <- (1, 21) [subsumption resolution 306,303]
308. ~1 | ~21 [avatar contradiction clause 307]
309. $false [avatar sat refutation 250,275,294,308]
% SZS output end Proof for 614545873428938748550888
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If alice is not tall or calm then fred is either not tall or not brave and vice versa.
Everyone who is brave is not kind.
Everyone who is wise or creative is both not quiet and brave and vice versa.
Everyone who is both funny and not strong is either happy or quiet and vice versa.
If someone is either wise or old then someone is not rich.
If someone is not old or generous then paul is both brave and kind and vice versa.
If lucy is both happy and not brave then someone is not rich or not calm and vice versa.
If someone is either not old or not brave then someone is not brave.
Everyone who is old is not rich and vice versa.
If susan is both not happy and curious then alice is not calm or wise and vice versa.
If fred is old or not strong then someone is happy or kind and vice versa.
If someone is brave or not creative then lucy is either tall or funny and vice versa.
If alice is quiet or not patient then someone is both tall and strong and vice versa.
Everyone who is both not curious and not kind is calm.
If john is both wise and not patient then paul is either not creative or not kind and vice versa.
John is both not calm and not brave.
Mary is both not patient and kind.
Someone is not happy or not generous.
Fred is both strong and humble.
Someone is brave.
Alice is rich or not wise.
Someone is either not strong or not calm. | Paul is not kind. | entailment | (((~tall(alice)|calm(alice)))<=>((~tall(fred)<~>~brave(fred))))&
(![X]:(brave(X)=>~kind(X)))&
(![X]:((wise(X)|creative(X))<=>(~quiet(X)&brave(X))))&
(![X]:((funny(X)&~strong(X))<=>(happy(X)<~>quiet(X))))&
((?[X]:((wise(X)<~>old(X))))=>(?[X]:(~rich(X))))&
((?[X]:((~old(X)|generous(X))))<=>((brave(paul)&kind(paul))))&
(((happy(lucy)&~brave(lucy)))<=>(?[X]:((~rich(X)|~calm(X)))))&
((?[X]:((~old(X)<~>~brave(X))))=>(?[X]:(~brave(X))))&
(![X]:(old(X)<=>~rich(X)))&
(((~happy(susan)&curious(susan)))<=>((~calm(alice)|wise(alice))))&
(((old(fred)|~strong(fred)))<=>(?[X]:((happy(X)|kind(X)))))&
((?[X]:((brave(X)|~creative(X))))<=>((tall(lucy)<~>funny(lucy))))&
(((quiet(alice)|~patient(alice)))<=>(?[X]:((tall(X)&strong(X)))))&
(![X]:((~curious(X)&~kind(X))=>calm(X)))&
(((wise(john)&~patient(john)))<=>((~creative(paul)<~>~kind(paul))))&
((~calm(john)&~brave(john)))&
((~patient(mary)&kind(mary)))&
(?[X]:((~happy(X)|~generous(X))))&
((strong(fred)&humble(fred)))&
(?[X]:(brave(X)))&
((rich(alice)|~wise(alice)))&
(?[X]:((~strong(X)<~>~calm(X)))) | ~kind(paul) | [
"p1",
"p2",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7308733412899343493174423
% SZS output start Proof for 7308733412899343493174423
2. ! [X0] : (brave(X0) => ~kind(X0)) [input p1]
3. ! [X0] : ((creative(X0) | wise(X0)) <=> (brave(X0) & ~quiet(X0))) [input p2]
15. (~patient(john) & wise(john)) <=> (~creative(paul) <~> ~kind(paul)) [input p14]
16. ~brave(john) & ~calm(john) [input p15]
23. kind(paul) [input hypothesis]
27. ! [X0] : (~kind(X0) | ~brave(X0)) [ennf transformation 2]
34. ! [X0] : (((creative(X0) | wise(X0)) | (~brave(X0) | quiet(X0))) & ((brave(X0) & ~quiet(X0)) | (~creative(X0) & ~wise(X0)))) [nnf transformation 3]
35. ! [X0] : ((creative(X0) | wise(X0) | ~brave(X0) | quiet(X0)) & ((brave(X0) & ~quiet(X0)) | (~creative(X0) & ~wise(X0)))) [flattening 34]
73. ((~patient(john) & wise(john)) | ((~creative(paul) | kind(paul)) & (~kind(paul) | creative(paul)))) & (((kind(paul) | creative(paul)) & (~kind(paul) | ~creative(paul))) | (patient(john) | ~wise(john))) [nnf transformation 15]
74. ((~patient(john) & wise(john)) | ((~creative(paul) | kind(paul)) & (~kind(paul) | creative(paul)))) & (((kind(paul) | creative(paul)) & (~kind(paul) | ~creative(paul))) | patient(john) | ~wise(john)) [flattening 73]
88. ~kind(X0) | ~brave(X0) [cnf transformation 27]
91. ~wise(X0) | brave(X0) [cnf transformation 35]
92. ~creative(X0) | brave(X0) [cnf transformation 35]
139. wise(john) | ~kind(paul) | creative(paul) [cnf transformation 74]
144. ~brave(john) [cnf transformation 16]
153. kind(paul) [cnf transformation 23]
192. 9 <=> kind(paul) [avatar definition]
194. kind(paul) <- (9) [avatar component clause 192]
201. 11 <=> brave(paul) [avatar definition]
202. ~brave(paul) <- (~11) [avatar component clause 201]
331. 39 <=> creative(paul) [avatar definition]
332. creative(paul) <- (39) [avatar component clause 331]
341. 41 <=> wise(john) [avatar definition]
343. wise(john) <- (41) [avatar component clause 341]
345. 39 | ~9 | 41 [avatar split clause 139,341,192,331]
373. 9 [avatar split clause 153,192]
388. ~brave(paul) <- (9) [resolution 88,194]
391. ~11 | ~9 [avatar split clause 388,192,201]
392. brave(paul) <- (39) [resolution 92,332]
393. $false <- (~11, 39) [subsumption resolution 392,202]
394. 11 | ~39 [avatar contradiction clause 393]
395. brave(john) <- (41) [resolution 343,91]
396. $false <- (41) [subsumption resolution 395,144]
397. ~41 [avatar contradiction clause 396]
398. $false [avatar sat refutation 345,373,391,394,397]
% SZS output end Proof for 7308733412899343493174423
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not calm is not funny and vice versa. If alice is not brave then someone is not patient or not funny and vice versa. Everyone who is either old or humble is patient or wise. Everyone who is funny or not tall is either rich or wise and vice versa. Everyone who is either not old or tall is either not generous or calm and vice versa. If alice is not calm or not curious then someone is either creative or not generous. Everyone who is not brave or not humble is either kind or creative and vice versa. Everyone who is not happy or not old is not curious or not strong and vice versa. If susan is both rich and funny then susan is quiet. If john is either not funny or curious then someone is strong or not generous. Everyone who is generous or brave is not kind or not tall and vice versa. Everyone who is not curious is generous. Everyone who is both not patient and old is not creative or curious. If someone is either not old or quiet then susan is both quiet and not strong and vice versa. Everyone who is either not quiet or not kind is not quiet or not tall. Everyone who is not calm or creative is not rich and vice versa. Someone is both not tall and humble. Paul is not quiet. Fred is either kind or not humble. Mary is not wise or kind. Alice is creative or not old. Paul is both curious and not generous. Paul is rich. Someone is generous or patient. | Mary is wise. | neutral | (![X]:(~calm(X)<=>~funny(X)))&
((~brave(alice))<=>(?[X]:((~patient(X)|~funny(X)))))&
(![X]:((old(X)<~>humble(X))=>(patient(X)|wise(X))))&
(![X]:((funny(X)|~tall(X))<=>(rich(X)<~>wise(X))))&
(![X]:((~old(X)<~>tall(X))<=>(~generous(X)<~>calm(X))))&
(((~calm(alice)|~curious(alice)))=>(?[X]:((creative(X)<~>~generous(X)))))&
(![X]:((~brave(X)|~humble(X))<=>(kind(X)<~>creative(X))))&
(![X]:((~happy(X)|~old(X))<=>(~curious(X)|~strong(X))))&
(((rich(susan)&funny(susan)))=>(quiet(susan)))&
(((~funny(john)<~>curious(john)))=>(?[X]:((strong(X)|~generous(X)))))&
(![X]:((generous(X)|brave(X))<=>(~kind(X)|~tall(X))))&
(![X]:(~curious(X)=>generous(X)))&
(![X]:((~patient(X)&old(X))=>(~creative(X)|curious(X))))&
((?[X]:((~old(X)<~>quiet(X))))<=>((quiet(susan)&~strong(susan))))&
(![X]:((~quiet(X)<~>~kind(X))=>(~quiet(X)|~tall(X))))&
(![X]:((~calm(X)|creative(X))<=>~rich(X)))&
(?[X]:((~tall(X)&humble(X))))&
(~quiet(paul))&
((kind(fred)<~>~humble(fred)))&
((~wise(mary)|kind(mary)))&
((creative(alice)|~old(alice)))&
((curious(paul)&~generous(paul)))&
(rich(paul))&
(?[X]:((generous(X)|patient(X)))) | wise(mary) | [] | null | 0 |
Everyone who is either tall or quiet is generous or creative.
If someone is both kind and wise then someone is calm and vice versa.
If someone is not curious or not old then someone is not strong.
Everyone who is not curious is patient.
If fred is both not generous and curious then someone is old and vice versa.
If someone is not brave or brave then paul is curious or not curious.
If susan is either calm or not patient then someone is not old or funny and vice versa.
If someone is not calm then someone is either not kind or strong.
If someone is both not brave and brave then someone is either old or not happy and vice versa.
If john is generous then someone is kind and vice versa.
Everyone who is either not old or old is both curious and not generous.
If someone is not brave or humble then someone is either not creative or not old.
If someone is not brave or not kind then susan is not creative or funny and vice versa.
Everyone who is both funny and generous is patient and vice versa.
Everyone who is either calm or not tall is not curious and vice versa.
If paul is kind or old then mary is brave or not strong.
Someone is either not strong or not calm.
Lucy is either generous or not quiet.
Someone is both not humble and brave.
Mary is both not rich and not patient. | Lucy is creative. | entailment | (![X]:((tall(X)<~>quiet(X))=>(generous(X)|creative(X))))&
((?[X]:((kind(X)&wise(X))))<=>(?[X]:(calm(X))))&
((?[X]:((~curious(X)|~old(X))))=>(?[X]:(~strong(X))))&
(![X]:(~curious(X)=>patient(X)))&
(((~generous(fred)&curious(fred)))<=>(?[X]:(old(X))))&
((?[X]:((~brave(X)|brave(X))))=>((curious(paul)|~curious(paul))))&
(((calm(susan)<~>~patient(susan)))<=>(?[X]:((~old(X)|funny(X)))))&
((?[X]:(~calm(X)))=>(?[X]:((~kind(X)<~>strong(X)))))&
((?[X]:((~brave(X)&brave(X))))<=>(?[X]:((old(X)<~>~happy(X)))))&
((generous(john))<=>(?[X]:(kind(X))))&
(![X]:((~old(X)<~>old(X))=>(curious(X)&~generous(X))))&
((?[X]:((~brave(X)|humble(X))))=>(?[X]:((~creative(X)<~>~old(X)))))&
((?[X]:((~brave(X)|~kind(X))))<=>((~creative(susan)|funny(susan))))&
(![X]:((funny(X)&generous(X))<=>patient(X)))&
(![X]:((calm(X)<~>~tall(X))<=>~curious(X)))&
(((kind(paul)|old(paul)))=>((brave(mary)|~strong(mary))))&
(?[X]:((~strong(X)<~>~calm(X))))&
((generous(lucy)<~>~quiet(lucy)))&
(?[X]:((~humble(X)&brave(X))))&
((~rich(mary)&~patient(mary))) | creative(lucy) | [
"p0",
"p1",
"p9",
"p10",
"p14",
"p17",
"hypothesis"
] | % SZS status Unsatisfiable for 2725056650474006522615676
% SZS output start Proof for 2725056650474006522615676
1. ! [X0] : ((tall(X0) <~> quiet(X0)) => (creative(X0) | generous(X0))) [input p0]
2. ? [X0] : (wise(X0) & kind(X0)) <=> ? [X0] : calm(X0) [input p1]
10. generous(john) <=> ? [X0] : kind(X0) [input p9]
11. ! [X0] : ((~old(X0) <~> old(X0)) => (~generous(X0) & curious(X0))) [input p10]
15. ! [X0] : ((calm(X0) <~> ~tall(X0)) <=> ~curious(X0)) [input p14]
18. generous(lucy) <~> ~quiet(lucy) [input p17]
21. ~creative(lucy) [input hypothesis]
22. ? [X0] : (wise(X0) & kind(X0)) <=> ? [X1] : calm(X1) [rectify 2]
30. ! [X0] : ((creative(X0) | generous(X0)) | (tall(X0) <=> quiet(X0))) [ennf transformation 1]
31. ! [X0] : (creative(X0) | generous(X0) | (tall(X0) <=> quiet(X0))) [flattening 30]
37. ! [X0] : ((~generous(X0) & curious(X0)) | (~old(X0) <=> old(X0))) [ennf transformation 11]
41. ! [X0] : (creative(X0) | generous(X0) | ((tall(X0) | ~quiet(X0)) & (quiet(X0) | ~tall(X0)))) [nnf transformation 31]
42. (? [X0] : (wise(X0) & kind(X0)) | ! [X1] : ~calm(X1)) & (? [X1] : calm(X1) | ! [X0] : (~wise(X0) | ~kind(X0))) [nnf transformation 22]
43. (? [X0] : (wise(X0) & kind(X0)) | ! [X1] : ~calm(X1)) & (? [X2] : calm(X2) | ! [X3] : (~wise(X3) | ~kind(X3))) [rectify 42]
44. ? [X0] : (wise(X0) & kind(X0)) => (wise(sK0) & kind(sK0)) [choice axiom]
45. ? [X2] : calm(X2) => calm(sK1) [choice axiom]
46. ((wise(sK0) & kind(sK0)) | ! [X1] : ~calm(X1)) & (calm(sK1) | ! [X3] : (~wise(X3) | ~kind(X3))) [skolemisation 43,45,44]
68. (generous(john) | ! [X0] : ~kind(X0)) & (? [X0] : kind(X0) | ~generous(john)) [nnf transformation 10]
69. (generous(john) | ! [X0] : ~kind(X0)) & (? [X1] : kind(X1) | ~generous(john)) [rectify 68]
70. ? [X1] : kind(X1) => kind(sK8) [choice axiom]
71. (generous(john) | ! [X0] : ~kind(X0)) & (kind(sK8) | ~generous(john)) [skolemisation 69,70]
72. ! [X0] : ((~generous(X0) & curious(X0)) | ((~old(X0) | ~old(X0)) & (old(X0) | old(X0)))) [nnf transformation 37]
84. ! [X0] : ((((tall(X0) | ~calm(X0)) & (~tall(X0) | calm(X0))) | curious(X0)) & (~curious(X0) | ((calm(X0) | tall(X0)) & (~tall(X0) | ~calm(X0))))) [nnf transformation 15]
88. (quiet(lucy) | ~generous(lucy)) & (~quiet(lucy) | generous(lucy)) [nnf transformation 18]
91. ~tall(X0) | generous(X0) | quiet(X0) | creative(X0) [cnf transformation 41]
94. kind(sK0) | ~calm(X1) [cnf transformation 46]
119. generous(john) | ~kind(X0) [cnf transformation 71]
120. curious(X0) | old(X0) | old(X0) [cnf transformation 72]
121. curious(X0) | ~old(X0) | ~old(X0) [cnf transformation 72]
122. ~generous(X0) | old(X0) | old(X0) [cnf transformation 72]
123. ~generous(X0) | ~old(X0) | ~old(X0) [cnf transformation 72]
134. ~curious(X0) | calm(X0) | tall(X0) [cnf transformation 84]
141. ~quiet(lucy) | generous(lucy) [cnf transformation 88]
145. ~creative(lucy) [cnf transformation 21]
146. curious(X0) | old(X0) [duplicate literal removal 120]
147. ~old(X0) | curious(X0) [duplicate literal removal 121]
148. ~generous(X0) | old(X0) [duplicate literal removal 122]
149. ~old(X0) | ~generous(X0) [duplicate literal removal 123]
151. 1 <=> ! [X1] : ~calm(X1) [avatar definition]
152. ~calm(X1) <- (1) [avatar component clause 151]
159. 3 <=> kind(sK0) [avatar definition]
161. kind(sK0) <- (3) [avatar component clause 159]
162. 1 | 3 [avatar split clause 94,159,151]
180. 8 <=> ! [X1] : curious(X1) [avatar definition]
181. curious(X1) <- (8) [avatar component clause 180]
254. 24 <=> ! [X0] : ~kind(X0) [avatar definition]
255. ~kind(X0) <- (24) [avatar component clause 254]
257. 25 <=> generous(john) [avatar definition]
259. generous(john) <- (25) [avatar component clause 257]
260. 24 | 25 [avatar split clause 119,257,254]
266. ~generous(X0) [subsumption resolution 148,149]
267. curious(X0) [subsumption resolution 146,147]
268. 8 [avatar split clause 267,180]
334. ~quiet(lucy) [subsumption resolution 141,266]
335. $false <- (3, 24) [subsumption resolution 161,255]
336. ~3 | ~24 [avatar contradiction clause 335]
350. calm(X0) | tall(X0) <- (8) [resolution 134,181]
351. tall(X0) <- (1, 8) [subsumption resolution 350,152]
353. generous(X0) | quiet(X0) | creative(X0) <- (1, 8) [resolution 91,351]
354. creative(X0) | quiet(X0) <- (1, 8) [subsumption resolution 353,266]
355. quiet(lucy) <- (1, 8) [resolution 354,145]
357. $false <- (1, 8) [subsumption resolution 355,334]
358. ~1 | ~8 [avatar contradiction clause 357]
359. $false <- (25) [subsumption resolution 259,266]
360. ~25 [avatar contradiction clause 359]
361. $false [avatar sat refutation 162,260,268,336,358,360]
% SZS output end Proof for 2725056650474006522615676
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
If susan is either humble or not curious then lucy is not rich or old and vice versa.
If someone is not brave or not humble then someone is not creative or rich and vice versa.
Everyone who is either not patient or humble is either old or curious and vice versa.
If john is both not brave and not funny then alice is either funny or patient and vice versa.
If someone is calm or wise then someone is not strong or calm.
Everyone who is both not happy and creative is wise or brave and vice versa.
Everyone who is either brave or not patient is either brave or wise.
Everyone who is happy or not wise is both brave and not brave and vice versa.
Everyone who is either funny or not kind is kind and vice versa.
Everyone who is not generous or quiet is both strong and not tall.
Everyone who is not rich or not tall is quiet or patient and vice versa.
If john is not generous then paul is both quiet and old and vice versa.
If someone is both funny and not humble then alice is both not quiet and tall and vice versa.
If susan is both happy and brave then someone is either calm or happy.
John is not happy.
Paul is either not quiet or old.
John is not calm or quiet.
Someone is not curious or generous.
Someone is either brave or strong.
Susan is either not kind or quiet. | John is not happy. | entailment | (((humble(susan)<~>~curious(susan)))<=>((~rich(lucy)|old(lucy))))&
((?[X]:((~brave(X)|~humble(X))))<=>(?[X]:((~creative(X)|rich(X)))))&
(![X]:((~patient(X)<~>humble(X))<=>(old(X)<~>curious(X))))&
(((~brave(john)&~funny(john)))<=>((funny(alice)<~>patient(alice))))&
((?[X]:((calm(X)|wise(X))))=>(?[X]:((~strong(X)|calm(X)))))&
(![X]:((~happy(X)&creative(X))<=>(wise(X)|brave(X))))&
(![X]:((brave(X)<~>~patient(X))=>(brave(X)<~>wise(X))))&
(![X]:((happy(X)|~wise(X))<=>(brave(X)&~brave(X))))&
(![X]:((funny(X)<~>~kind(X))<=>kind(X)))&
(![X]:((~generous(X)|quiet(X))=>(strong(X)&~tall(X))))&
(![X]:((~rich(X)|~tall(X))<=>(quiet(X)|patient(X))))&
((~generous(john))<=>((quiet(paul)&old(paul))))&
((?[X]:((funny(X)&~humble(X))))<=>((~quiet(alice)&tall(alice))))&
(((happy(susan)&brave(susan)))=>(?[X]:((calm(X)<~>happy(X)))))&
(~happy(john))&
((~quiet(paul)<~>old(paul)))&
((~calm(john)|quiet(john)))&
(?[X]:((~curious(X)|generous(X))))&
(?[X]:((brave(X)<~>strong(X))))&
((~kind(susan)<~>quiet(susan))) | ~happy(john) | [
"p5",
"p7",
"hypothesis"
] | % SZS status Unsatisfiable for 1151305066916051073341433
% SZS output start Proof for 1151305066916051073341433
6. ! [X0] : ((creative(X0) & ~happy(X0)) <=> (brave(X0) | wise(X0))) [input p5]
8. ! [X0] : ((~wise(X0) | happy(X0)) <=> (~brave(X0) & brave(X0))) [input p7]
21. happy(john) [input hypothesis]
42. ! [X0] : (((creative(X0) & ~happy(X0)) | (~brave(X0) & ~wise(X0))) & ((brave(X0) | wise(X0)) | (~creative(X0) | happy(X0)))) [nnf transformation 6]
43. ! [X0] : (((creative(X0) & ~happy(X0)) | (~brave(X0) & ~wise(X0))) & (brave(X0) | wise(X0) | ~creative(X0) | happy(X0))) [flattening 42]
45. ! [X0] : (((~wise(X0) | happy(X0)) | (brave(X0) | ~brave(X0))) & ((~brave(X0) & brave(X0)) | (wise(X0) & ~happy(X0)))) [nnf transformation 8]
46. ! [X0] : ((~wise(X0) | happy(X0) | brave(X0) | ~brave(X0)) & ((~brave(X0) & brave(X0)) | (wise(X0) & ~happy(X0)))) [flattening 45]
95. ~happy(X0) | ~brave(X0) [cnf transformation 43]
102. brave(X0) | ~happy(X0) [cnf transformation 46]
137. happy(john) [cnf transformation 21]
235. ~happy(X0) [subsumption resolution 102,95]
310. $false [subsumption resolution 137,235]
% SZS output end Proof for 1151305066916051073341433
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.033 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either funny or not humble is patient or not generous and vice versa.
Everyone who is humble or kind is both calm and tall and vice versa.
Everyone who is both generous and not brave is either creative or not creative and vice versa.
If someone is either calm or wise then fred is both rich and not curious.
Everyone who is both not rich and not quiet is strong or not creative and vice versa.
If mary is not tall or funny then susan is both not happy and kind and vice versa.
Everyone who is humble is both rich and patient.
If someone is both not tall and not patient then someone is both curious and not rich and vice versa.
Everyone who is old or not calm is both not calm and humble.
Everyone who is both old and not curious is happy or not rich and vice versa.
If fred is both old and kind then someone is both tall and not brave.
Everyone who is either not old or rich is not kind or not rich and vice versa.
If susan is not wise then lucy is either calm or not curious and vice versa.
Everyone who is either not creative or not curious is patient.
Everyone who is rich is creative or not happy.
If mary is brave then someone is either strong or happy and vice versa.
Fred is either tall or not wise.
Someone is either rich or happy.
Alice is either creative or not generous.
Someone is both kind and not wise.
Someone is either not generous or not quiet.
Fred is rich.
Someone is old or rich.
Someone is strong or not old. | Susan is humble. | neutral | (![X]:((funny(X)<~>~humble(X))<=>(patient(X)|~generous(X))))&
(![X]:((humble(X)|kind(X))<=>(calm(X)&tall(X))))&
(![X]:((generous(X)&~brave(X))<=>(creative(X)<~>~creative(X))))&
((?[X]:((calm(X)<~>wise(X))))=>((rich(fred)&~curious(fred))))&
(![X]:((~rich(X)&~quiet(X))<=>(strong(X)|~creative(X))))&
(((~tall(mary)|funny(mary)))<=>((~happy(susan)&kind(susan))))&
(![X]:(humble(X)=>(rich(X)&patient(X))))&
((?[X]:((~tall(X)&~patient(X))))<=>(?[X]:((curious(X)&~rich(X)))))&
(![X]:((old(X)|~calm(X))=>(~calm(X)&humble(X))))&
(![X]:((old(X)&~curious(X))<=>(happy(X)|~rich(X))))&
(((old(fred)&kind(fred)))=>(?[X]:((tall(X)&~brave(X)))))&
(![X]:((~old(X)<~>rich(X))<=>(~kind(X)|~rich(X))))&
((~wise(susan))<=>((calm(lucy)<~>~curious(lucy))))&
(![X]:((~creative(X)<~>~curious(X))=>patient(X)))&
(![X]:(rich(X)=>(creative(X)|~happy(X))))&
((brave(mary))<=>(?[X]:((strong(X)<~>happy(X)))))&
((tall(fred)<~>~wise(fred)))&
(?[X]:((rich(X)<~>happy(X))))&
((creative(alice)<~>~generous(alice)))&
(?[X]:((kind(X)&~wise(X))))&
(?[X]:((~generous(X)<~>~quiet(X))))&
(rich(fred))&
(?[X]:((old(X)|rich(X))))&
(?[X]:((strong(X)|~old(X)))) | humble(susan) | [] | null | 0 |
If someone is both brave and not happy then mary is not humble or old and vice versa.
If someone is wise then john is both brave and humble.
Everyone who is humble is either not old or not curious.
Everyone who is both funny and not kind is both quiet and creative and vice versa.
Everyone who is not wise is strong or not kind.
If mary is either creative or not curious then someone is strong or not quiet and vice versa.
If paul is not tall then someone is either brave or kind.
If paul is either not patient or not rich then mary is both quiet and not generous.
If susan is patient then susan is either happy or not generous.
Everyone who is humble is calm or happy.
Everyone who is old or not brave is strong.
Everyone who is either creative or not patient is rich or strong.
If someone is not wise then mary is not humble or not curious and vice versa.
Everyone who is either kind or happy is not quiet or patient and vice versa.
Everyone who is both not patient and funny is either kind or not kind and vice versa.
Everyone who is both not funny and brave is quiet and vice versa.
Someone is both generous and rich.
Fred is both humble and tall.
Someone is both wise and generous.
Paul is funny or calm.
Fred is both not creative and not old.
Someone is either quiet or not calm.
Someone is either not wise or not curious. | Susan is not happy. | entailment | ((?[X]:((brave(X)&~happy(X))))<=>((~humble(mary)|old(mary))))&
((?[X]:(wise(X)))=>((brave(john)&humble(john))))&
(![X]:(humble(X)=>(~old(X)<~>~curious(X))))&
(![X]:((funny(X)&~kind(X))<=>(quiet(X)&creative(X))))&
(![X]:(~wise(X)=>(strong(X)|~kind(X))))&
(((creative(mary)<~>~curious(mary)))<=>(?[X]:((strong(X)|~quiet(X)))))&
((~tall(paul))=>(?[X]:((brave(X)<~>kind(X)))))&
(((~patient(paul)<~>~rich(paul)))=>((quiet(mary)&~generous(mary))))&
((patient(susan))=>((happy(susan)<~>~generous(susan))))&
(![X]:(humble(X)=>(calm(X)|happy(X))))&
(![X]:((old(X)|~brave(X))=>strong(X)))&
(![X]:((creative(X)<~>~patient(X))=>(rich(X)|strong(X))))&
((?[X]:(~wise(X)))<=>((~humble(mary)|~curious(mary))))&
(![X]:((kind(X)<~>happy(X))<=>(~quiet(X)|patient(X))))&
(![X]:((~patient(X)&funny(X))<=>(kind(X)<~>~kind(X))))&
(![X]:((~funny(X)&brave(X))<=>quiet(X)))&
(?[X]:((generous(X)&rich(X))))&
((humble(fred)&tall(fred)))&
(?[X]:((wise(X)&generous(X))))&
((funny(paul)|calm(paul)))&
((~creative(fred)&~old(fred)))&
(?[X]:((quiet(X)<~>~calm(X))))&
(?[X]:((~wise(X)<~>~curious(X)))) | ~happy(susan) | [
"p3",
"p13",
"p14",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 217296076748580375279686
% SZS output start Proof for 217296076748580375279686
4. ! [X0] : ((~kind(X0) & funny(X0)) <=> (creative(X0) & quiet(X0))) [input p3]
14. ! [X0] : ((kind(X0) <~> happy(X0)) <=> (patient(X0) | ~quiet(X0))) [input p13]
15. ! [X0] : ((funny(X0) & ~patient(X0)) <=> (kind(X0) <~> ~kind(X0))) [input p14]
16. ! [X0] : ((brave(X0) & ~funny(X0)) <=> quiet(X0)) [input p15]
24. happy(susan) [input hypothesis]
44. ! [X0] : (((~kind(X0) & funny(X0)) | (~creative(X0) | ~quiet(X0))) & ((creative(X0) & quiet(X0)) | (kind(X0) | ~funny(X0)))) [nnf transformation 4]
45. ! [X0] : (((~kind(X0) & funny(X0)) | ~creative(X0) | ~quiet(X0)) & ((creative(X0) & quiet(X0)) | kind(X0) | ~funny(X0))) [flattening 44]
58. ! [X0] : ((((~happy(X0) | ~kind(X0)) & (happy(X0) | kind(X0))) | (~patient(X0) & quiet(X0))) & ((patient(X0) | ~quiet(X0)) | ((kind(X0) | ~happy(X0)) & (happy(X0) | ~kind(X0))))) [nnf transformation 14]
59. ! [X0] : ((((~happy(X0) | ~kind(X0)) & (happy(X0) | kind(X0))) | (~patient(X0) & quiet(X0))) & (patient(X0) | ~quiet(X0) | ((kind(X0) | ~happy(X0)) & (happy(X0) | ~kind(X0))))) [flattening 58]
60. ! [X0] : (((funny(X0) & ~patient(X0)) | ((kind(X0) | kind(X0)) & (~kind(X0) | ~kind(X0)))) & (((kind(X0) | ~kind(X0)) & (~kind(X0) | kind(X0))) | (~funny(X0) | patient(X0)))) [nnf transformation 15]
61. ! [X0] : (((funny(X0) & ~patient(X0)) | ((kind(X0) | kind(X0)) & (~kind(X0) | ~kind(X0)))) & (((kind(X0) | ~kind(X0)) & (~kind(X0) | kind(X0))) | ~funny(X0) | patient(X0))) [flattening 60]
62. ! [X0] : (((brave(X0) & ~funny(X0)) | ~quiet(X0)) & (quiet(X0) | (~brave(X0) | funny(X0)))) [nnf transformation 16]
63. ! [X0] : (((brave(X0) & ~funny(X0)) | ~quiet(X0)) & (quiet(X0) | ~brave(X0) | funny(X0))) [flattening 62]
83. ~funny(X0) | kind(X0) | quiet(X0) [cnf transformation 45]
112. ~kind(X0) | ~happy(X0) | quiet(X0) [cnf transformation 59]
118. funny(X0) | ~kind(X0) | ~kind(X0) [cnf transformation 61]
119. funny(X0) | kind(X0) | kind(X0) [cnf transformation 61]
121. ~funny(X0) | ~quiet(X0) [cnf transformation 63]
135. happy(susan) [cnf transformation 24]
138. funny(X0) | ~kind(X0) [duplicate literal removal 118]
139. kind(X0) | funny(X0) [duplicate literal removal 119]
230. 20 <=> happy(susan) [avatar definition]
231. happy(susan) <- (20) [avatar component clause 230]
249. funny(X0) [subsumption resolution 138,139]
251. ~quiet(X0) [subsumption resolution 121,249]
263. 20 [avatar split clause 135,230]
278. kind(X0) | quiet(X0) [resolution 83,249]
279. kind(X0) [subsumption resolution 278,251]
309. ~happy(X0) | quiet(X0) [resolution 112,279]
311. ~happy(X0) [subsumption resolution 309,251]
312. $false <- (20) [resolution 311,231]
317. ~20 [avatar contradiction clause 312]
318. $false [avatar sat refutation 263,317]
% SZS output end Proof for 217296076748580375279686
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both creative and wise is generous.
Everyone who is not kind is not curious or creative and vice versa.
If john is not calm then someone is not wise.
If someone is strong or kind then fred is not happy and vice versa.
Everyone who is not strong or kind is not calm and vice versa.
Everyone who is either not humble or not rich is both not old and patient and vice versa.
Everyone who is either not rich or not happy is either not happy or rich.
Everyone who is either old or quiet is both kind and funny.
If alice is wise or humble then mary is strong.
Everyone who is funny or brave is wise.
Everyone who is either brave or not rich is not brave.
Everyone who is not humble or rich is both generous and not humble.
Everyone who is both not wise and patient is quiet and vice versa.
If lucy is either not funny or happy then someone is not funny or not rich.
If john is curious then susan is curious.
Everyone who is both brave and tall is rich or not happy.
Alice is patient.
Lucy is both not funny and not strong.
Mary is not wise.
Mary is either not patient or funny.
Someone is happy or curious.
Someone is either calm or happy. | Fred is not wise. | neutral | (![X]:((creative(X)&wise(X))=>generous(X)))&
(![X]:(~kind(X)<=>(~curious(X)|creative(X))))&
((~calm(john))=>(?[X]:(~wise(X))))&
((?[X]:((strong(X)|kind(X))))<=>(~happy(fred)))&
(![X]:((~strong(X)|kind(X))<=>~calm(X)))&
(![X]:((~humble(X)<~>~rich(X))<=>(~old(X)&patient(X))))&
(![X]:((~rich(X)<~>~happy(X))=>(~happy(X)<~>rich(X))))&
(![X]:((old(X)<~>quiet(X))=>(kind(X)&funny(X))))&
(((wise(alice)|humble(alice)))=>(strong(mary)))&
(![X]:((funny(X)|brave(X))=>wise(X)))&
(![X]:((brave(X)<~>~rich(X))=>~brave(X)))&
(![X]:((~humble(X)|rich(X))=>(generous(X)&~humble(X))))&
(![X]:((~wise(X)&patient(X))<=>quiet(X)))&
(((~funny(lucy)<~>happy(lucy)))=>(?[X]:((~funny(X)|~rich(X)))))&
((curious(john))=>(curious(susan)))&
(![X]:((brave(X)&tall(X))=>(rich(X)|~happy(X))))&
(patient(alice))&
((~funny(lucy)&~strong(lucy)))&
(~wise(mary))&
((~patient(mary)<~>funny(mary)))&
(?[X]:((happy(X)|curious(X))))&
(?[X]:((calm(X)<~>happy(X)))) | ~wise(fred) | [] | null | 0 |
If john is both generous and old then mary is strong and vice versa.
If paul is both kind and brave then mary is calm.
If john is not happy then mary is both happy and not quiet.
If alice is both wise and not kind then alice is both happy and quiet and vice versa.
If someone is calm then someone is either quiet or wise and vice versa.
Everyone who is brave or not strong is both generous and not creative and vice versa.
If someone is calm then john is happy or patient and vice versa.
If someone is kind then someone is strong or not generous.
Everyone who is both not creative and humble is both not old and curious and vice versa.
If someone is not happy or not kind then john is both generous and not quiet.
Everyone who is not wise is not patient or happy.
Everyone who is curious or not strong is either not old or wise.
Everyone who is wise or not wise is both not curious and not wise.
Everyone who is not strong is not quiet or not rich and vice versa.
If paul is creative then someone is both rich and curious.
Everyone who is both not generous and old is patient or funny and vice versa.
Someone is both calm and generous.
Alice is both not generous and humble.
Someone is either creative or not rich.
Paul is both calm and generous.
Someone is tall or not happy.
Someone is either curious or funny.
Someone is either not kind or not calm. | John is curious. | contradiction | (((generous(john)&old(john)))<=>(strong(mary)))&
(((kind(paul)&brave(paul)))=>(calm(mary)))&
((~happy(john))=>((happy(mary)&~quiet(mary))))&
(((wise(alice)&~kind(alice)))<=>((happy(alice)&quiet(alice))))&
((?[X]:(calm(X)))<=>(?[X]:((quiet(X)<~>wise(X)))))&
(![X]:((brave(X)|~strong(X))<=>(generous(X)&~creative(X))))&
((?[X]:(calm(X)))<=>((happy(john)|patient(john))))&
((?[X]:(kind(X)))=>(?[X]:((strong(X)|~generous(X)))))&
(![X]:((~creative(X)&humble(X))<=>(~old(X)&curious(X))))&
((?[X]:((~happy(X)|~kind(X))))=>((generous(john)&~quiet(john))))&
(![X]:(~wise(X)=>(~patient(X)|happy(X))))&
(![X]:((curious(X)|~strong(X))=>(~old(X)<~>wise(X))))&
(![X]:((wise(X)|~wise(X))=>(~curious(X)&~wise(X))))&
(![X]:(~strong(X)<=>(~quiet(X)|~rich(X))))&
((creative(paul))=>(?[X]:((rich(X)&curious(X)))))&
(![X]:((~generous(X)&old(X))<=>(patient(X)|funny(X))))&
(?[X]:((calm(X)&generous(X))))&
((~generous(alice)&humble(alice)))&
(?[X]:((creative(X)<~>~rich(X))))&
((calm(paul)&generous(paul)))&
(?[X]:((tall(X)|~happy(X))))&
(?[X]:((curious(X)<~>funny(X))))&
(?[X]:((~kind(X)<~>~calm(X)))) | curious(john) | [
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 4553418270505248422284258
% SZS output start Proof for 4553418270505248422284258
13. ! [X0] : ((~wise(X0) | wise(X0)) => (~wise(X0) & ~curious(X0))) [input p12]
24. curious(john) [input hypothesis]
36. ! [X0] : ((~wise(X0) & ~curious(X0)) | (wise(X0) & ~wise(X0))) [ennf transformation 13]
114. ~curious(X0) | wise(X0) [cnf transformation 36]
115. ~wise(X0) | ~wise(X0) [cnf transformation 36]
139. curious(john) [cnf transformation 24]
140. ~wise(X0) [duplicate literal removal 115]
262. ~curious(X0) [subsumption resolution 114,140]
285. $false [subsumption resolution 139,262]
% SZS output end Proof for 4553418270505248422284258
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either patient or rich is either patient or curious. Everyone who is not generous or patient is not tall. Everyone who is either not curious or not old is both not generous and wise and vice versa. If susan is either not wise or patient then someone is either not rich or not generous. Everyone who is both creative and not kind is wise or not old and vice versa. Everyone who is either not generous or not calm is both not tall and not curious and vice versa. Everyone who is both not strong and creative is either old or not funny and vice versa. If someone is kind or humble then alice is not old. If someone is not creative or not curious then someone is not patient. Everyone who is either humble or not wise is not creative or not patient. If alice is not tall then someone is either patient or quiet and vice versa. If someone is not rich or not curious then someone is both not creative and not curious. If mary is either not tall or not rich then alice is both funny and quiet. Everyone who is kind or not brave is either strong or not old and vice versa. If lucy is not tall then someone is rich or not creative and vice versa. If susan is wise then paul is not strong or not quiet and vice versa. Mary is not generous or not rich. Paul is tall or old. Someone is both not tall and not funny. Paul is both tall and happy. Alice is generous or creative. Lucy is both patient and not funny. | Susan is wise. | neutral | (![X]:((patient(X)<~>rich(X))=>(patient(X)<~>curious(X))))&
(![X]:((~generous(X)|patient(X))=>~tall(X)))&
(![X]:((~curious(X)<~>~old(X))<=>(~generous(X)&wise(X))))&
(((~wise(susan)<~>patient(susan)))=>(?[X]:((~rich(X)<~>~generous(X)))))&
(![X]:((creative(X)&~kind(X))<=>(wise(X)|~old(X))))&
(![X]:((~generous(X)<~>~calm(X))<=>(~tall(X)&~curious(X))))&
(![X]:((~strong(X)&creative(X))<=>(old(X)<~>~funny(X))))&
((?[X]:((kind(X)|humble(X))))=>(~old(alice)))&
((?[X]:((~creative(X)|~curious(X))))=>(?[X]:(~patient(X))))&
(![X]:((humble(X)<~>~wise(X))=>(~creative(X)|~patient(X))))&
((~tall(alice))<=>(?[X]:((patient(X)<~>quiet(X)))))&
((?[X]:((~rich(X)|~curious(X))))=>(?[X]:((~creative(X)&~curious(X)))))&
(((~tall(mary)<~>~rich(mary)))=>((funny(alice)&quiet(alice))))&
(![X]:((kind(X)|~brave(X))<=>(strong(X)<~>~old(X))))&
((~tall(lucy))<=>(?[X]:((rich(X)|~creative(X)))))&
((wise(susan))<=>((~strong(paul)|~quiet(paul))))&
((~generous(mary)|~rich(mary)))&
((tall(paul)|old(paul)))&
(?[X]:((~tall(X)&~funny(X))))&
((tall(paul)&happy(paul)))&
((generous(alice)|creative(alice)))&
((patient(lucy)&~funny(lucy))) | wise(susan) | [] | null | 0 |
Everyone who is not patient or wise is both old and strong.
Everyone who is either calm or curious is old and vice versa.
If someone is old then mary is both wise and not old and vice versa.
Everyone who is either rich or generous is either not happy or tall and vice versa.
If someone is either curious or not creative then someone is not curious and vice versa.
Everyone who is happy is not calm or not curious.
If lucy is kind or calm then someone is either not kind or rich.
If susan is either not humble or not rich then someone is not generous or generous and vice versa.
Everyone who is both not curious and funny is either not humble or happy and vice versa.
Everyone who is both not patient and not strong is either not tall or funny.
If john is both not rich and curious then someone is both kind and not strong.
Everyone who is brave or humble is not old and vice versa.
If someone is wise then someone is both creative and old and vice versa.
Everyone who is both rich and tall is either patient or not curious.
If alice is either creative or generous then paul is calm or not calm and vice versa.
Everyone who is calm is not humble or not brave and vice versa.
Someone is funny or not calm.
Someone is funny.
Someone is kind or not brave.
Someone is generous or quiet.
Susan is calm or wise.
Alice is not calm. | Alice is curious. | contradiction | (![X]:((~patient(X)|wise(X))=>(old(X)&strong(X))))&
(![X]:((calm(X)<~>curious(X))<=>old(X)))&
((?[X]:(old(X)))<=>((wise(mary)&~old(mary))))&
(![X]:((rich(X)<~>generous(X))<=>(~happy(X)<~>tall(X))))&
((?[X]:((curious(X)<~>~creative(X))))<=>(?[X]:(~curious(X))))&
(![X]:(happy(X)=>(~calm(X)|~curious(X))))&
(((kind(lucy)|calm(lucy)))=>(?[X]:((~kind(X)<~>rich(X)))))&
(((~humble(susan)<~>~rich(susan)))<=>(?[X]:((~generous(X)|generous(X)))))&
(![X]:((~curious(X)&funny(X))<=>(~humble(X)<~>happy(X))))&
(![X]:((~patient(X)&~strong(X))=>(~tall(X)<~>funny(X))))&
(((~rich(john)&curious(john)))=>(?[X]:((kind(X)&~strong(X)))))&
(![X]:((brave(X)|humble(X))<=>~old(X)))&
((?[X]:(wise(X)))<=>(?[X]:((creative(X)&old(X)))))&
(![X]:((rich(X)&tall(X))=>(patient(X)<~>~curious(X))))&
(((creative(alice)<~>generous(alice)))<=>((calm(paul)|~calm(paul))))&
(![X]:(calm(X)<=>(~humble(X)|~brave(X))))&
(?[X]:((funny(X)|~calm(X))))&
(?[X]:(funny(X)))&
(?[X]:((kind(X)|~brave(X))))&
(?[X]:((generous(X)|quiet(X))))&
((calm(susan)|wise(susan)))&
(~calm(alice)) | curious(alice) | [
"p0",
"p1",
"p2",
"p21",
"hypothesis"
] | % SZS status Unsatisfiable for 4667384994925725657472435
% SZS output start Proof for 4667384994925725657472435
1. ! [X0] : ((wise(X0) | ~patient(X0)) => (strong(X0) & old(X0))) [input p0]
2. ! [X0] : ((calm(X0) <~> curious(X0)) <=> old(X0)) [input p1]
3. ? [X0] : old(X0) <=> (~old(mary) & wise(mary)) [input p2]
22. ~calm(alice) [input p21]
23. curious(alice) [input hypothesis]
27. ! [X0] : ((strong(X0) & old(X0)) | (~wise(X0) & patient(X0))) [ennf transformation 1]
37. ! [X0] : ((((~curious(X0) | ~calm(X0)) & (curious(X0) | calm(X0))) | ~old(X0)) & (old(X0) | ((calm(X0) | ~curious(X0)) & (curious(X0) | ~calm(X0))))) [nnf transformation 2]
38. (? [X0] : old(X0) | (old(mary) | ~wise(mary))) & ((~old(mary) & wise(mary)) | ! [X0] : ~old(X0)) [nnf transformation 3]
39. (? [X0] : old(X0) | old(mary) | ~wise(mary)) & ((~old(mary) & wise(mary)) | ! [X0] : ~old(X0)) [flattening 38]
40. (? [X0] : old(X0) | old(mary) | ~wise(mary)) & ((~old(mary) & wise(mary)) | ! [X1] : ~old(X1)) [rectify 39]
41. ? [X0] : old(X0) => old(sK0) [choice axiom]
42. (old(sK0) | old(mary) | ~wise(mary)) & ((~old(mary) & wise(mary)) | ! [X1] : ~old(X1)) [skolemisation 40,41]
80. ~wise(X0) | old(X0) [cnf transformation 27]
84. ~curious(X0) | calm(X0) | old(X0) [cnf transformation 37]
87. wise(mary) | ~old(X1) [cnf transformation 42]
88. ~old(mary) | ~old(X1) [cnf transformation 42]
144. ~calm(alice) [cnf transformation 22]
145. curious(alice) [cnf transformation 23]
147. 1 <=> ! [X1] : ~old(X1) [avatar definition]
148. ~old(X1) <- (1) [avatar component clause 147]
150. 2 <=> old(mary) [avatar definition]
153. 1 | ~2 [avatar split clause 88,150,147]
155. 3 <=> wise(mary) [avatar definition]
157. wise(mary) <- (3) [avatar component clause 155]
158. 1 | 3 [avatar split clause 87,155,147]
307. old(mary) <- (3) [resolution 80,157]
310. 2 | ~3 [avatar split clause 307,155,150]
328. calm(alice) | old(alice) [resolution 84,145]
329. old(alice) [subsumption resolution 328,144]
330. $false <- (1) [subsumption resolution 329,148]
331. ~1 [avatar contradiction clause 330]
332. $false [avatar sat refutation 153,158,310,331]
% SZS output end Proof for 4667384994925725657472435
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.030 s
% ------------------------------
% ------------------------------
| 0 |
If someone is both generous and not quiet then someone is not patient.
If someone is kind or patient then someone is not generous or not curious.
Everyone who is not curious is strong or not patient and vice versa.
If john is both brave and not rich then alice is both happy and curious.
Everyone who is not rich is both creative and kind and vice versa.
Everyone who is either not creative or creative is both brave and funny and vice versa.
Everyone who is not brave or not strong is wise or not creative.
Everyone who is either not quiet or not brave is wise and vice versa.
Everyone who is not kind is either calm or not calm and vice versa.
Everyone who is curious or strong is not funny or not kind and vice versa.
Everyone who is both not generous and strong is both curious and wise and vice versa.
If someone is both not creative and strong then fred is both old and not happy and vice versa.
Everyone who is both not tall and happy is not kind and vice versa.
Everyone who is not funny or strong is either not tall or brave.
Everyone who is not quiet or not tall is not happy or rich and vice versa.
If mary is not brave then paul is not humble.
Lucy is either not brave or calm.
Susan is either patient or not generous.
Susan is both not tall and rich.
Someone is kind or humble. | Paul is curious. | entailment | ((?[X]:((generous(X)&~quiet(X))))=>(?[X]:(~patient(X))))&
((?[X]:((kind(X)|patient(X))))=>(?[X]:((~generous(X)|~curious(X)))))&
(![X]:(~curious(X)<=>(strong(X)|~patient(X))))&
(((brave(john)&~rich(john)))=>((happy(alice)&curious(alice))))&
(![X]:(~rich(X)<=>(creative(X)&kind(X))))&
(![X]:((~creative(X)<~>creative(X))<=>(brave(X)&funny(X))))&
(![X]:((~brave(X)|~strong(X))=>(wise(X)|~creative(X))))&
(![X]:((~quiet(X)<~>~brave(X))<=>wise(X)))&
(![X]:(~kind(X)<=>(calm(X)<~>~calm(X))))&
(![X]:((curious(X)|strong(X))<=>(~funny(X)|~kind(X))))&
(![X]:((~generous(X)&strong(X))<=>(curious(X)&wise(X))))&
((?[X]:((~creative(X)&strong(X))))<=>((old(fred)&~happy(fred))))&
(![X]:((~tall(X)&happy(X))<=>~kind(X)))&
(![X]:((~funny(X)|strong(X))=>(~tall(X)<~>brave(X))))&
(![X]:((~quiet(X)|~tall(X))<=>(~happy(X)|rich(X))))&
((~brave(mary))=>(~humble(paul)))&
((~brave(lucy)<~>calm(lucy)))&
((patient(susan)<~>~generous(susan)))&
((~tall(susan)&rich(susan)))&
(?[X]:((kind(X)|humble(X)))) | curious(paul) | [
"p5",
"p8",
"p9",
"p12",
"p13",
"hypothesis"
] | % SZS status Unsatisfiable for 2323520774639897964726498
% SZS output start Proof for 2323520774639897964726498
6. ! [X0] : ((~creative(X0) <~> creative(X0)) <=> (funny(X0) & brave(X0))) [input p5]
9. ! [X0] : (~kind(X0) <=> (calm(X0) <~> ~calm(X0))) [input p8]
10. ! [X0] : ((strong(X0) | curious(X0)) <=> (~kind(X0) | ~funny(X0))) [input p9]
13. ! [X0] : ((happy(X0) & ~tall(X0)) <=> ~kind(X0)) [input p12]
14. ! [X0] : ((strong(X0) | ~funny(X0)) => (~tall(X0) <~> brave(X0))) [input p13]
21. ~curious(paul) [input hypothesis]
30. ! [X0] : ((~tall(X0) <~> brave(X0)) | (~strong(X0) & funny(X0))) [ennf transformation 14]
42. ! [X0] : ((((~creative(X0) | creative(X0)) & (creative(X0) | ~creative(X0))) | (~funny(X0) | ~brave(X0))) & ((funny(X0) & brave(X0)) | ((~creative(X0) | ~creative(X0)) & (creative(X0) | creative(X0))))) [nnf transformation 6]
43. ! [X0] : ((((~creative(X0) | creative(X0)) & (creative(X0) | ~creative(X0))) | ~funny(X0) | ~brave(X0)) & ((funny(X0) & brave(X0)) | ((~creative(X0) | ~creative(X0)) & (creative(X0) | creative(X0))))) [flattening 42]
45. ! [X0] : ((~kind(X0) | ((calm(X0) | calm(X0)) & (~calm(X0) | ~calm(X0)))) & (((calm(X0) | ~calm(X0)) & (~calm(X0) | calm(X0))) | kind(X0))) [nnf transformation 9]
46. ! [X0] : (((strong(X0) | curious(X0)) | (kind(X0) & funny(X0))) & ((~kind(X0) | ~funny(X0)) | (~strong(X0) & ~curious(X0)))) [nnf transformation 10]
47. ! [X0] : ((strong(X0) | curious(X0) | (kind(X0) & funny(X0))) & (~kind(X0) | ~funny(X0) | (~strong(X0) & ~curious(X0)))) [flattening 46]
55. ! [X0] : (((happy(X0) & ~tall(X0)) | kind(X0)) & (~kind(X0) | (~happy(X0) | tall(X0)))) [nnf transformation 13]
56. ! [X0] : (((happy(X0) & ~tall(X0)) | kind(X0)) & (~kind(X0) | ~happy(X0) | tall(X0))) [flattening 55]
57. ! [X0] : (((~brave(X0) | tall(X0)) & (brave(X0) | ~tall(X0))) | (~strong(X0) & funny(X0))) [nnf transformation 30]
75. brave(X0) | creative(X0) | creative(X0) [cnf transformation 43]
76. brave(X0) | ~creative(X0) | ~creative(X0) [cnf transformation 43]
89. ~kind(X0) | ~calm(X0) | ~calm(X0) [cnf transformation 45]
90. ~kind(X0) | calm(X0) | calm(X0) [cnf transformation 45]
94. strong(X0) | curious(X0) | kind(X0) [cnf transformation 47]
104. ~tall(X0) | kind(X0) [cnf transformation 56]
109. ~brave(X0) | tall(X0) | ~strong(X0) [cnf transformation 57]
122. ~curious(paul) [cnf transformation 21]
123. ~kind(X0) | ~calm(X0) [duplicate literal removal 89]
124. ~kind(X0) | calm(X0) [duplicate literal removal 90]
125. brave(X0) | creative(X0) [duplicate literal removal 75]
126. ~creative(X0) | brave(X0) [duplicate literal removal 76]
150. 6 <=> ! [X1] : ~kind(X1) [avatar definition]
151. ~kind(X1) <- (6) [avatar component clause 150]
172. brave(X0) [subsumption resolution 125,126]
175. ~kind(X0) [subsumption resolution 123,124]
176. 6 [avatar split clause 175,150]
204. ~strong(X0) | tall(X0) [subsumption resolution 109,172]
245. curious(X0) | kind(X0) | tall(X0) [resolution 94,204]
251. tall(X0) | curious(X0) <- (6) [subsumption resolution 245,151]
283. curious(X2) | kind(X2) <- (6) [resolution 251,104]
284. curious(X2) <- (6) [subsumption resolution 283,151]
301. $false <- (6) [resolution 284,122]
305. ~6 [avatar contradiction clause 301]
306. $false [avatar sat refutation 176,305]
% SZS output end Proof for 2323520774639897964726498
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either old or calm then someone is both not curious and wise and vice versa. Everyone who is curious is either curious or brave. If alice is both not brave and tall then someone is not patient and vice versa. Everyone who is old is both wise and not kind and vice versa. If someone is both not brave and brave then lucy is both old and funny and vice versa. Everyone who is not calm or not tall is not kind. If lucy is either funny or not happy then someone is both quiet and creative and vice versa. If fred is brave or not curious then someone is not calm and vice versa. If someone is not tall or not rich then john is calm or old. If someone is not funny or not tall then alice is both patient and brave. If susan is either not brave or not happy then someone is rich. If mary is both patient and not patient then susan is rich or not strong. Everyone who is not calm or not brave is either kind or funny and vice versa. If fred is tall or not funny then lucy is happy or rich. If someone is not wise then someone is either funny or rich. If someone is funny then someone is not brave or not generous and vice versa. John is both not tall and not rich. Paul is tall or not calm. Someone is either not curious or brave. Someone is both funny and calm. Mary is rich or not tall. Paul is not strong or calm. Someone is not rich or patient. Someone is both strong and patient. | Alice is brave. | entailment | ((?[X]:((old(X)<~>calm(X))))<=>(?[X]:((~curious(X)&wise(X)))))&
(![X]:(curious(X)=>(curious(X)<~>brave(X))))&
(((~brave(alice)&tall(alice)))<=>(?[X]:(~patient(X))))&
(![X]:(old(X)<=>(wise(X)&~kind(X))))&
((?[X]:((~brave(X)&brave(X))))<=>((old(lucy)&funny(lucy))))&
(![X]:((~calm(X)|~tall(X))=>~kind(X)))&
(((funny(lucy)<~>~happy(lucy)))<=>(?[X]:((quiet(X)&creative(X)))))&
(((brave(fred)|~curious(fred)))<=>(?[X]:(~calm(X))))&
((?[X]:((~tall(X)|~rich(X))))=>((calm(john)|old(john))))&
((?[X]:((~funny(X)|~tall(X))))=>((patient(alice)&brave(alice))))&
(((~brave(susan)<~>~happy(susan)))=>(?[X]:(rich(X))))&
(((patient(mary)&~patient(mary)))=>((rich(susan)|~strong(susan))))&
(![X]:((~calm(X)|~brave(X))<=>(kind(X)<~>funny(X))))&
(((tall(fred)|~funny(fred)))=>((happy(lucy)|rich(lucy))))&
((?[X]:(~wise(X)))=>(?[X]:((funny(X)<~>rich(X)))))&
((?[X]:(funny(X)))<=>(?[X]:((~brave(X)|~generous(X)))))&
((~tall(john)&~rich(john)))&
((tall(paul)|~calm(paul)))&
(?[X]:((~curious(X)<~>brave(X))))&
(?[X]:((funny(X)&calm(X))))&
((rich(mary)|~tall(mary)))&
((~strong(paul)|calm(paul)))&
(?[X]:((~rich(X)|patient(X))))&
(?[X]:((strong(X)&patient(X)))) | brave(alice) | [
"p9",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 5909942728716005055109027
% SZS output start Proof for 5909942728716005055109027
10. ? [X0] : (~tall(X0) | ~funny(X0)) => (brave(alice) & patient(alice)) [input p9]
17. ~rich(john) & ~tall(john) [input p16]
25. ~brave(alice) [input hypothesis]
33. (brave(alice) & patient(alice)) | ! [X0] : (tall(X0) & funny(X0)) [ennf transformation 10]
124. brave(alice) | tall(X0) [cnf transformation 33]
141. ~tall(john) [cnf transformation 17]
153. ~brave(alice) [cnf transformation 25]
195. 10 <=> brave(alice) [avatar definition]
271. 26 <=> ! [X0] : tall(X0) [avatar definition]
272. tall(X0) <- (26) [avatar component clause 271]
274. 26 | 10 [avatar split clause 124,195,271]
386. ~10 [avatar split clause 153,195]
393. $false <- (26) [resolution 272,141]
394. ~26 [avatar contradiction clause 393]
395. $false [avatar sat refutation 274,386,394]
% SZS output end Proof for 5909942728716005055109027
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
If someone is either not brave or calm then someone is funny or strong and vice versa.
Everyone who is not kind is not happy and vice versa.
Everyone who is either not wise or not old is happy or kind.
Everyone who is creative is both not creative and not happy.
Everyone who is humble or not wise is not curious or strong and vice versa.
Everyone who is not kind or not tall is either not creative or not happy and vice versa.
Everyone who is not patient is either not curious or humble and vice versa.
Everyone who is both tall and not generous is either not brave or brave.
Everyone who is creative is not kind or not patient.
Everyone who is either not funny or creative is both not rich and wise and vice versa.
If someone is both not wise and not calm then someone is humble or not kind and vice versa.
Everyone who is either not brave or quiet is either tall or not happy.
Everyone who is either curious or tall is rich or not strong.
If alice is both rich and not patient then mary is both brave and strong.
Everyone who is either quiet or calm is not humble or not strong.
Everyone who is either not humble or calm is both happy and funny and vice versa.
Someone is not old.
Someone is creative or old.
Paul is not funny.
Someone is funny.
Someone is kind or brave.
Susan is not patient or not humble. | Alice is generous. | neutral | ((?[X]:((~brave(X)<~>calm(X))))<=>(?[X]:((funny(X)|strong(X)))))&
(![X]:(~kind(X)<=>~happy(X)))&
(![X]:((~wise(X)<~>~old(X))=>(happy(X)|kind(X))))&
(![X]:(creative(X)=>(~creative(X)&~happy(X))))&
(![X]:((humble(X)|~wise(X))<=>(~curious(X)|strong(X))))&
(![X]:((~kind(X)|~tall(X))<=>(~creative(X)<~>~happy(X))))&
(![X]:(~patient(X)<=>(~curious(X)<~>humble(X))))&
(![X]:((tall(X)&~generous(X))=>(~brave(X)<~>brave(X))))&
(![X]:(creative(X)=>(~kind(X)|~patient(X))))&
(![X]:((~funny(X)<~>creative(X))<=>(~rich(X)&wise(X))))&
((?[X]:((~wise(X)&~calm(X))))<=>(?[X]:((humble(X)|~kind(X)))))&
(![X]:((~brave(X)<~>quiet(X))=>(tall(X)<~>~happy(X))))&
(![X]:((curious(X)<~>tall(X))=>(rich(X)|~strong(X))))&
(((rich(alice)&~patient(alice)))=>((brave(mary)&strong(mary))))&
(![X]:((quiet(X)<~>calm(X))=>(~humble(X)|~strong(X))))&
(![X]:((~humble(X)<~>calm(X))<=>(happy(X)&funny(X))))&
(?[X]:(~old(X)))&
(?[X]:((creative(X)|old(X))))&
(~funny(paul))&
(?[X]:(funny(X)))&
(?[X]:((kind(X)|brave(X))))&
((~patient(susan)|~humble(susan))) | generous(alice) | [] | null | 0 |
Everyone who is strong is generous and vice versa.
If susan is both kind and not wise then someone is not kind and vice versa.
Everyone who is not tall is not quiet and vice versa.
Everyone who is both not funny and not creative is not rich and vice versa.
If someone is both not humble and not strong then someone is either kind or not happy and vice versa.
Everyone who is either creative or not old is both happy and tall.
Everyone who is not strong is kind.
Everyone who is both not creative and humble is either humble or not generous and vice versa.
Everyone who is curious or not rich is old or brave.
Everyone who is wise or not brave is old or not rich and vice versa.
If someone is both not brave and brave then someone is not wise.
If susan is both wise and not funny then fred is brave and vice versa.
Everyone who is both not happy and strong is either wise or tall and vice versa.
If someone is creative then lucy is either happy or not kind and vice versa.
Everyone who is either not tall or funny is either brave or not wise.
If someone is both not happy and not tall then someone is either not happy or strong.
Someone is both not kind and not rich.
Someone is both wise and humble.
Someone is quiet.
Susan is both not rich and not creative.
John is either not brave or happy.
Paul is wise. | John is humble. | neutral | (![X]:(strong(X)<=>generous(X)))&
(((kind(susan)&~wise(susan)))<=>(?[X]:(~kind(X))))&
(![X]:(~tall(X)<=>~quiet(X)))&
(![X]:((~funny(X)&~creative(X))<=>~rich(X)))&
((?[X]:((~humble(X)&~strong(X))))<=>(?[X]:((kind(X)<~>~happy(X)))))&
(![X]:((creative(X)<~>~old(X))=>(happy(X)&tall(X))))&
(![X]:(~strong(X)=>kind(X)))&
(![X]:((~creative(X)&humble(X))<=>(humble(X)<~>~generous(X))))&
(![X]:((curious(X)|~rich(X))=>(old(X)|brave(X))))&
(![X]:((wise(X)|~brave(X))<=>(old(X)|~rich(X))))&
((?[X]:((~brave(X)&brave(X))))=>(?[X]:(~wise(X))))&
(((wise(susan)&~funny(susan)))<=>(brave(fred)))&
(![X]:((~happy(X)&strong(X))<=>(wise(X)<~>tall(X))))&
((?[X]:(creative(X)))<=>((happy(lucy)<~>~kind(lucy))))&
(![X]:((~tall(X)<~>funny(X))=>(brave(X)<~>~wise(X))))&
((?[X]:((~happy(X)&~tall(X))))=>(?[X]:((~happy(X)<~>strong(X)))))&
(?[X]:((~kind(X)&~rich(X))))&
(?[X]:((wise(X)&humble(X))))&
(?[X]:(quiet(X)))&
((~rich(susan)&~creative(susan)))&
((~brave(john)<~>happy(john)))&
(wise(paul)) | humble(john) | [] | null | 0 |
Everyone who is either not kind or kind is both not brave and calm and vice versa.
If paul is either strong or not humble then someone is both not strong and not brave.
Everyone who is both not old and generous is either not old or patient and vice versa.
Everyone who is not brave is either kind or curious.
If mary is rich or not wise then someone is both patient and not tall.
If someone is tall then susan is curious.
If someone is not brave or generous then alice is either not old or not tall and vice versa.
If fred is both tall and not kind then susan is creative and vice versa.
Everyone who is happy is not quiet.
Everyone who is both patient and kind is not patient or patient.
Everyone who is both not tall and not humble is not wise and vice versa.
Everyone who is not happy or not patient is both not happy and generous.
If mary is patient then someone is both creative and not kind and vice versa.
Everyone who is not patient is wise and vice versa.
Everyone who is not strong or not generous is not strong or not brave and vice versa.
If someone is generous then someone is not funny or generous and vice versa.
Someone is not patient or calm.
Paul is either quiet or brave.
Fred is either not strong or not brave.
Lucy is either rich or not generous.
Someone is happy or not strong.
Alice is not generous or creative.
Someone is either patient or not tall.
Someone is creative. | Alice is not tall. | neutral | (![X]:((~kind(X)<~>kind(X))<=>(~brave(X)&calm(X))))&
(((strong(paul)<~>~humble(paul)))=>(?[X]:((~strong(X)&~brave(X)))))&
(![X]:((~old(X)&generous(X))<=>(~old(X)<~>patient(X))))&
(![X]:(~brave(X)=>(kind(X)<~>curious(X))))&
(((rich(mary)|~wise(mary)))=>(?[X]:((patient(X)&~tall(X)))))&
((?[X]:(tall(X)))=>(curious(susan)))&
((?[X]:((~brave(X)|generous(X))))<=>((~old(alice)<~>~tall(alice))))&
(((tall(fred)&~kind(fred)))<=>(creative(susan)))&
(![X]:(happy(X)=>~quiet(X)))&
(![X]:((patient(X)&kind(X))=>(~patient(X)|patient(X))))&
(![X]:((~tall(X)&~humble(X))<=>~wise(X)))&
(![X]:((~happy(X)|~patient(X))=>(~happy(X)&generous(X))))&
((patient(mary))<=>(?[X]:((creative(X)&~kind(X)))))&
(![X]:(~patient(X)<=>wise(X)))&
(![X]:((~strong(X)|~generous(X))<=>(~strong(X)|~brave(X))))&
((?[X]:(generous(X)))<=>(?[X]:((~funny(X)|generous(X)))))&
(?[X]:((~patient(X)|calm(X))))&
((quiet(paul)<~>brave(paul)))&
((~strong(fred)<~>~brave(fred)))&
((rich(lucy)<~>~generous(lucy)))&
(?[X]:((happy(X)|~strong(X))))&
((~generous(alice)|creative(alice)))&
(?[X]:((patient(X)<~>~tall(X))))&
(?[X]:(creative(X))) | ~tall(alice) | [] | null | 0 |
Everyone who is not humble or humble is not kind or not rich and vice versa.
If someone is either quiet or kind then john is either old or not creative and vice versa.
If someone is both calm and not patient then someone is both patient and wise and vice versa.
If someone is either quiet or not rich then someone is either not funny or tall.
If alice is kind or not calm then lucy is patient or not rich.
If susan is not brave or not quiet then someone is not strong or not old.
If someone is not tall or humble then someone is kind.
Everyone who is not patient is not happy or generous and vice versa.
Everyone who is either not tall or not generous is not rich.
Everyone who is creative or wise is generous and vice versa.
Everyone who is old is not calm and vice versa.
If someone is both patient and kind then mary is both not calm and not funny and vice versa.
Everyone who is not wise or old is not patient and vice versa.
Everyone who is both not tall and humble is both quiet and creative.
Everyone who is brave is either not calm or not tall.
If someone is not curious then fred is brave or funny and vice versa.
Someone is not brave.
Fred is both strong and not rich.
Susan is not humble.
Susan is both not kind and not calm.
Someone is both generous and wise.
Someone is humble. | Mary is not old. | contradiction | (![X]:((~humble(X)|humble(X))<=>(~kind(X)|~rich(X))))&
((?[X]:((quiet(X)<~>kind(X))))<=>((old(john)<~>~creative(john))))&
((?[X]:((calm(X)&~patient(X))))<=>(?[X]:((patient(X)&wise(X)))))&
((?[X]:((quiet(X)<~>~rich(X))))=>(?[X]:((~funny(X)<~>tall(X)))))&
(((kind(alice)|~calm(alice)))=>((patient(lucy)|~rich(lucy))))&
(((~brave(susan)|~quiet(susan)))=>(?[X]:((~strong(X)|~old(X)))))&
((?[X]:((~tall(X)|humble(X))))=>(?[X]:(kind(X))))&
(![X]:(~patient(X)<=>(~happy(X)|generous(X))))&
(![X]:((~tall(X)<~>~generous(X))=>~rich(X)))&
(![X]:((creative(X)|wise(X))<=>generous(X)))&
(![X]:(old(X)<=>~calm(X)))&
((?[X]:((patient(X)&kind(X))))<=>((~calm(mary)&~funny(mary))))&
(![X]:((~wise(X)|old(X))<=>~patient(X)))&
(![X]:((~tall(X)&humble(X))=>(quiet(X)&creative(X))))&
(![X]:(brave(X)=>(~calm(X)<~>~tall(X))))&
((?[X]:(~curious(X)))<=>((brave(fred)|funny(fred))))&
(?[X]:(~brave(X)))&
((strong(fred)&~rich(fred)))&
(~humble(susan))&
((~kind(susan)&~calm(susan)))&
(?[X]:((generous(X)&wise(X))))&
(?[X]:(humble(X))) | ~old(mary) | [
"p2",
"p7",
"p9",
"p10",
"p12",
"hypothesis"
] | % SZS status Unsatisfiable for 5875330322466841361996262
% SZS output start Proof for 5875330322466841361996262
3. ? [X0] : (~patient(X0) & calm(X0)) <=> ? [X0] : (wise(X0) & patient(X0)) [input p2]
8. ! [X0] : (~patient(X0) <=> (generous(X0) | ~happy(X0))) [input p7]
10. ! [X0] : ((wise(X0) | creative(X0)) <=> generous(X0)) [input p9]
11. ! [X0] : (old(X0) <=> ~calm(X0)) [input p10]
13. ! [X0] : ((old(X0) | ~wise(X0)) <=> ~patient(X0)) [input p12]
23. ~old(mary) [input hypothesis]
24. ? [X0] : (~patient(X0) & calm(X0)) <=> ? [X1] : (wise(X1) & patient(X1)) [rectify 3]
42. (? [X0] : (~patient(X0) & calm(X0)) | ! [X1] : (~wise(X1) | ~patient(X1))) & (? [X1] : (wise(X1) & patient(X1)) | ! [X0] : (patient(X0) | ~calm(X0))) [nnf transformation 24]
43. (? [X0] : (~patient(X0) & calm(X0)) | ! [X1] : (~wise(X1) | ~patient(X1))) & (? [X2] : (wise(X2) & patient(X2)) | ! [X3] : (patient(X3) | ~calm(X3))) [rectify 42]
44. ? [X0] : (~patient(X0) & calm(X0)) => (~patient(sK1) & calm(sK1)) [choice axiom]
45. ? [X2] : (wise(X2) & patient(X2)) => (wise(sK2) & patient(sK2)) [choice axiom]
46. ((~patient(sK1) & calm(sK1)) | ! [X1] : (~wise(X1) | ~patient(X1))) & ((wise(sK2) & patient(sK2)) | ! [X3] : (patient(X3) | ~calm(X3))) [skolemisation 43,45,44]
56. ! [X0] : ((~patient(X0) | (~generous(X0) & happy(X0))) & ((generous(X0) | ~happy(X0)) | patient(X0))) [nnf transformation 8]
57. ! [X0] : ((~patient(X0) | (~generous(X0) & happy(X0))) & (generous(X0) | ~happy(X0) | patient(X0))) [flattening 56]
59. ! [X0] : (((wise(X0) | creative(X0)) | ~generous(X0)) & (generous(X0) | (~wise(X0) & ~creative(X0)))) [nnf transformation 10]
60. ! [X0] : ((wise(X0) | creative(X0) | ~generous(X0)) & (generous(X0) | (~wise(X0) & ~creative(X0)))) [flattening 59]
61. ! [X0] : ((old(X0) | calm(X0)) & (~calm(X0) | ~old(X0))) [nnf transformation 11]
67. ! [X0] : (((old(X0) | ~wise(X0)) | patient(X0)) & (~patient(X0) | (~old(X0) & wise(X0)))) [nnf transformation 13]
68. ! [X0] : ((old(X0) | ~wise(X0) | patient(X0)) & (~patient(X0) | (~old(X0) & wise(X0)))) [flattening 67]
93. patient(sK2) | patient(X3) | ~calm(X3) [cnf transformation 46]
94. wise(sK2) | patient(X3) | ~calm(X3) [cnf transformation 46]
95. calm(sK1) | ~wise(X1) | ~patient(X1) [cnf transformation 46]
96. ~patient(sK1) | ~wise(X1) | ~patient(X1) [cnf transformation 46]
109. ~generous(X0) | ~patient(X0) [cnf transformation 57]
113. ~wise(X0) | generous(X0) [cnf transformation 60]
116. calm(X0) | old(X0) [cnf transformation 61]
121. ~patient(X0) | wise(X0) [cnf transformation 68]
140. ~old(mary) [cnf transformation 23]
173. 7 <=> ! [X1] : (~wise(X1) | ~patient(X1)) [avatar definition]
174. ~wise(X1) | ~patient(X1) <- (7) [avatar component clause 173]
176. 8 <=> patient(sK1) [avatar definition]
178. ~patient(sK1) <- (~8) [avatar component clause 176]
179. 7 | ~8 [avatar split clause 96,176,173]
181. 9 <=> calm(sK1) [avatar definition]
183. calm(sK1) <- (9) [avatar component clause 181]
184. 7 | 9 [avatar split clause 95,181,173]
186. 10 <=> ! [X3] : (patient(X3) | ~calm(X3)) [avatar definition]
187. ~calm(X3) | patient(X3) <- (10) [avatar component clause 186]
189. 11 <=> wise(sK2) [avatar definition]
191. wise(sK2) <- (11) [avatar component clause 189]
192. 10 | 11 [avatar split clause 94,189,186]
194. 12 <=> patient(sK2) [avatar definition]
197. 10 | 12 [avatar split clause 93,194,186]
265. 28 <=> calm(mary) [avatar definition]
266. ~calm(mary) <- (~28) [avatar component clause 265]
267. calm(mary) <- (28) [avatar component clause 265]
313. old(mary) <- (~28) [resolution 116,266]
315. $false <- (~28) [subsumption resolution 313,140]
316. 28 [avatar contradiction clause 315]
321. patient(sK1) <- (9, 10) [resolution 187,183]
324. $false <- (~8, 9, 10) [subsumption resolution 321,178]
325. 8 | ~9 | ~10 [avatar contradiction clause 324]
326. generous(sK2) <- (11) [resolution 191,113]
335. ~patient(sK2) <- (11) [resolution 326,109]
338. ~12 | ~11 [avatar split clause 335,189,194]
339. ~patient(X1) <- (7) [subsumption resolution 174,121]
347. patient(mary) <- (10, 28) [resolution 187,267]
349. $false <- (7, 10, 28) [subsumption resolution 347,339]
350. ~7 | ~10 | ~28 [avatar contradiction clause 349]
352. $false [avatar sat refutation 179,184,192,197,316,325,338,350]
% SZS output end Proof for 5875330322466841361996262
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is generous is not curious.
If mary is wise or quiet then someone is both not generous and not patient and vice versa.
If lucy is either wise or not old then someone is not funny and vice versa.
Everyone who is either quiet or calm is patient or not happy and vice versa.
If someone is either curious or not strong then someone is not funny or not curious and vice versa.
Everyone who is not strong or not tall is both not patient and not old and vice versa.
If someone is both curious and funny then paul is not kind.
If fred is both not creative and old then mary is both humble and not kind.
If susan is either humble or not happy then alice is both not tall and not happy.
Everyone who is both not old and not happy is not humble or tall and vice versa.
If alice is strong then alice is humble and vice versa.
Everyone who is both wise and creative is patient and vice versa.
If someone is kind or not tall then fred is both not patient and quiet.
Everyone who is both creative and strong is either not calm or not strong and vice versa.
If susan is either brave or calm then someone is not humble.
Everyone who is not tall or strong is both quiet and not strong and vice versa.
Alice is either not curious or not kind.
Someone is not kind.
Susan is old or not old.
John is either not strong or not generous.
Fred is brave or not quiet.
Someone is not funny.
Someone is either calm or not creative. | Susan is humble. | contradiction | (![X]:(generous(X)=>~curious(X)))&
(((wise(mary)|quiet(mary)))<=>(?[X]:((~generous(X)&~patient(X)))))&
(((wise(lucy)<~>~old(lucy)))<=>(?[X]:(~funny(X))))&
(![X]:((quiet(X)<~>calm(X))<=>(patient(X)|~happy(X))))&
((?[X]:((curious(X)<~>~strong(X))))<=>(?[X]:((~funny(X)|~curious(X)))))&
(![X]:((~strong(X)|~tall(X))<=>(~patient(X)&~old(X))))&
((?[X]:((curious(X)&funny(X))))=>(~kind(paul)))&
(((~creative(fred)&old(fred)))=>((humble(mary)&~kind(mary))))&
(((humble(susan)<~>~happy(susan)))=>((~tall(alice)&~happy(alice))))&
(![X]:((~old(X)&~happy(X))<=>(~humble(X)|tall(X))))&
((strong(alice))<=>(humble(alice)))&
(![X]:((wise(X)&creative(X))<=>patient(X)))&
((?[X]:((kind(X)|~tall(X))))=>((~patient(fred)&quiet(fred))))&
(![X]:((creative(X)&strong(X))<=>(~calm(X)<~>~strong(X))))&
(((brave(susan)<~>calm(susan)))=>(?[X]:(~humble(X))))&
(![X]:((~tall(X)|strong(X))<=>(quiet(X)&~strong(X))))&
((~curious(alice)<~>~kind(alice)))&
(?[X]:(~kind(X)))&
((old(susan)|~old(susan)))&
((~strong(john)<~>~generous(john)))&
((brave(fred)|~quiet(fred)))&
(?[X]:(~funny(X)))&
(?[X]:((calm(X)<~>~creative(X)))) | humble(susan) | [
"p3",
"p5",
"p9",
"p13",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7223744205499797009584706
% SZS output start Proof for 7223744205499797009584706
4. ! [X0] : ((quiet(X0) <~> calm(X0)) <=> (~happy(X0) | patient(X0))) [input p3]
6. ! [X0] : ((~tall(X0) | ~strong(X0)) <=> (~old(X0) & ~patient(X0))) [input p5]
10. ! [X0] : ((~happy(X0) & ~old(X0)) <=> (tall(X0) | ~humble(X0))) [input p9]
14. ! [X0] : ((strong(X0) & creative(X0)) <=> (~calm(X0) <~> ~strong(X0))) [input p13]
16. ! [X0] : ((strong(X0) | ~tall(X0)) <=> (~strong(X0) & quiet(X0))) [input p15]
24. humble(susan) [input hypothesis]
42. ! [X0] : ((((~calm(X0) | ~quiet(X0)) & (calm(X0) | quiet(X0))) | (happy(X0) & ~patient(X0))) & ((~happy(X0) | patient(X0)) | ((quiet(X0) | ~calm(X0)) & (calm(X0) | ~quiet(X0))))) [nnf transformation 4]
43. ! [X0] : ((((~calm(X0) | ~quiet(X0)) & (calm(X0) | quiet(X0))) | (happy(X0) & ~patient(X0))) & (~happy(X0) | patient(X0) | ((quiet(X0) | ~calm(X0)) & (calm(X0) | ~quiet(X0))))) [flattening 42]
49. ! [X0] : (((~tall(X0) | ~strong(X0)) | (old(X0) | patient(X0))) & ((~old(X0) & ~patient(X0)) | (tall(X0) & strong(X0)))) [nnf transformation 6]
50. ! [X0] : ((~tall(X0) | ~strong(X0) | old(X0) | patient(X0)) & ((~old(X0) & ~patient(X0)) | (tall(X0) & strong(X0)))) [flattening 49]
52. ! [X0] : (((~happy(X0) & ~old(X0)) | (~tall(X0) & humble(X0))) & ((tall(X0) | ~humble(X0)) | (happy(X0) | old(X0)))) [nnf transformation 10]
53. ! [X0] : (((~happy(X0) & ~old(X0)) | (~tall(X0) & humble(X0))) & (tall(X0) | ~humble(X0) | happy(X0) | old(X0))) [flattening 52]
57. ! [X0] : (((strong(X0) & creative(X0)) | ((~calm(X0) | strong(X0)) & (~strong(X0) | calm(X0)))) & (((strong(X0) | calm(X0)) & (~strong(X0) | ~calm(X0))) | (~strong(X0) | ~creative(X0)))) [nnf transformation 14]
58. ! [X0] : (((strong(X0) & creative(X0)) | ((~calm(X0) | strong(X0)) & (~strong(X0) | calm(X0)))) & (((strong(X0) | calm(X0)) & (~strong(X0) | ~calm(X0))) | ~strong(X0) | ~creative(X0))) [flattening 57]
62. ! [X0] : (((strong(X0) | ~tall(X0)) | (strong(X0) | ~quiet(X0))) & ((~strong(X0) & quiet(X0)) | (~strong(X0) & tall(X0)))) [nnf transformation 16]
63. ! [X0] : ((strong(X0) | ~tall(X0) | strong(X0) | ~quiet(X0)) & ((~strong(X0) & quiet(X0)) | (~strong(X0) & tall(X0)))) [flattening 62]
83. ~happy(X0) | patient(X0) | calm(X0) | ~quiet(X0) [cnf transformation 43]
86. happy(X0) | quiet(X0) | calm(X0) [cnf transformation 43]
95. ~patient(X0) | strong(X0) [cnf transformation 50]
98. ~old(X0) | tall(X0) [cnf transformation 50]
107. tall(X0) | ~humble(X0) | happy(X0) | old(X0) [cnf transformation 53]
109. ~old(X0) | ~tall(X0) [cnf transformation 53]
111. ~tall(X0) | ~happy(X0) [cnf transformation 53]
126. strong(X0) | ~calm(X0) | strong(X0) [cnf transformation 58]
129. tall(X0) | quiet(X0) [cnf transformation 63]
132. ~strong(X0) | ~strong(X0) [cnf transformation 63]
133. strong(X0) | ~tall(X0) | strong(X0) | ~quiet(X0) [cnf transformation 63]
144. humble(susan) [cnf transformation 24]
145. ~strong(X0) [duplicate literal removal 132]
146. ~tall(X0) | strong(X0) | ~quiet(X0) [duplicate literal removal 133]
148. ~calm(X0) | strong(X0) [duplicate literal removal 126]
250. 23 <=> happy(susan) [avatar definition]
251. ~happy(susan) <- (~23) [avatar component clause 250]
252. happy(susan) <- (23) [avatar component clause 250]
254. 24 <=> humble(susan) [avatar definition]
256. humble(susan) <- (24) [avatar component clause 254]
269. ~old(X0) [subsumption resolution 109,98]
270. ~humble(X0) | tall(X0) | happy(X0) [subsumption resolution 107,269]
301. 33 <=> calm(susan) [avatar definition]
302. calm(susan) <- (33) [avatar component clause 301]
303. ~calm(susan) <- (~33) [avatar component clause 301]
332. 24 [avatar split clause 144,254]
335. ~happy(X0) | quiet(X0) [resolution 129,111]
336. quiet(susan) | calm(susan) <- (~23) [resolution 86,251]
340. 39 <=> quiet(susan) [avatar definition]
342. quiet(susan) <- (39) [avatar component clause 340]
343. 33 | 39 | 23 [avatar split clause 336,250,340,301]
348. strong(susan) <- (33) [resolution 302,148]
349. $false <- (33) [subsumption resolution 348,145]
350. ~33 [avatar contradiction clause 349]
392. tall(susan) | happy(susan) <- (24) [resolution 270,256]
393. tall(susan) <- (~23, 24) [subsumption resolution 392,251]
394. strong(susan) | ~quiet(susan) <- (~23, 24) [resolution 393,146]
396. ~quiet(susan) <- (~23, 24) [subsumption resolution 394,145]
397. $false <- (~23, 24, 39) [subsumption resolution 396,342]
398. 23 | ~24 | ~39 [avatar contradiction clause 397]
406. quiet(susan) <- (23) [resolution 335,252]
409. patient(susan) | calm(susan) | ~quiet(susan) <- (23) [resolution 83,252]
411. patient(susan) | ~quiet(susan) <- (23, ~33) [subsumption resolution 409,303]
412. patient(susan) <- (23, ~33, 39) [subsumption resolution 411,342]
417. strong(susan) <- (23, ~33, 39) [resolution 412,95]
419. $false <- (23, ~33, 39) [subsumption resolution 417,145]
420. ~23 | 33 | ~39 [avatar contradiction clause 419]
426. 39 | ~23 [avatar split clause 406,250,340]
427. $false [avatar sat refutation 332,343,350,398,420,426]
% SZS output end Proof for 7223744205499797009584706
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not patient is strong and vice versa.
Everyone who is not strong or strong is both not patient and not wise.
Everyone who is old or not tall is not rich or patient and vice versa.
Everyone who is either rich or not rich is not humble or patient.
If mary is not funny or brave then john is both not kind and happy.
If lucy is kind then someone is not calm or not old.
If susan is both not wise and not calm then lucy is either brave or wise.
Everyone who is generous is not patient.
If someone is funny then susan is tall.
Everyone who is not strong is not humble.
If someone is both old and kind then john is both not creative and not quiet and vice versa.
If someone is either not generous or calm then someone is either patient or generous and vice versa.
Everyone who is not generous or not curious is not strong.
If someone is both happy and not wise then paul is curious and vice versa.
If lucy is curious then alice is both not creative and not patient and vice versa.
Someone is both creative and not calm.
Someone is not tall.
Fred is not strong or not calm.
Someone is not calm.
Lucy is either not humble or not curious.
Someone is calm or kind.
John is old or calm. | Alice is creative. | contradiction | (![X]:(~patient(X)<=>strong(X)))&
(![X]:((~strong(X)|strong(X))=>(~patient(X)&~wise(X))))&
(![X]:((old(X)|~tall(X))<=>(~rich(X)|patient(X))))&
(![X]:((rich(X)<~>~rich(X))=>(~humble(X)|patient(X))))&
(((~funny(mary)|brave(mary)))=>((~kind(john)&happy(john))))&
((kind(lucy))=>(?[X]:((~calm(X)|~old(X)))))&
(((~wise(susan)&~calm(susan)))=>((brave(lucy)<~>wise(lucy))))&
(![X]:(generous(X)=>~patient(X)))&
((?[X]:(funny(X)))=>(tall(susan)))&
(![X]:(~strong(X)=>~humble(X)))&
((?[X]:((old(X)&kind(X))))<=>((~creative(john)&~quiet(john))))&
((?[X]:((~generous(X)<~>calm(X))))<=>(?[X]:((patient(X)<~>generous(X)))))&
(![X]:((~generous(X)|~curious(X))=>~strong(X)))&
((?[X]:((happy(X)&~wise(X))))<=>(curious(paul)))&
((curious(lucy))<=>((~creative(alice)&~patient(alice))))&
(?[X]:((creative(X)&~calm(X))))&
(?[X]:(~tall(X)))&
((~strong(fred)|~calm(fred)))&
(?[X]:(~calm(X)))&
((~humble(lucy)<~>~curious(lucy)))&
(?[X]:((calm(X)|kind(X))))&
((old(john)|calm(john))) | creative(alice) | [
"p0",
"p1",
"p12",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 8718588814050403256659536
% SZS output start Proof for 8718588814050403256659536
1. ! [X0] : (~patient(X0) <=> strong(X0)) [input p0]
2. ! [X0] : ((strong(X0) | ~strong(X0)) => (~wise(X0) & ~patient(X0))) [input p1]
13. ! [X0] : ((~curious(X0) | ~generous(X0)) => ~strong(X0)) [input p12]
15. curious(lucy) <=> (~patient(alice) & ~creative(alice)) [input p14]
23. creative(alice) [input hypothesis]
25. ! [X0] : ((~wise(X0) & ~patient(X0)) | (~strong(X0) & strong(X0))) [ennf transformation 2]
35. ! [X0] : (~strong(X0) | (curious(X0) & generous(X0))) [ennf transformation 13]
36. ! [X0] : ((~patient(X0) | ~strong(X0)) & (strong(X0) | patient(X0))) [nnf transformation 1]
57. (curious(lucy) | (patient(alice) | creative(alice))) & ((~patient(alice) & ~creative(alice)) | ~curious(lucy)) [nnf transformation 15]
58. (curious(lucy) | patient(alice) | creative(alice)) & ((~patient(alice) & ~creative(alice)) | ~curious(lucy)) [flattening 57]
68. strong(X0) | patient(X0) [cnf transformation 36]
70. ~patient(X0) | strong(X0) [cnf transformation 25]
103. ~strong(X0) | curious(X0) [cnf transformation 35]
107. ~creative(alice) | ~curious(lucy) [cnf transformation 58]
119. creative(alice) [cnf transformation 23]
123. strong(X0) [subsumption resolution 70,68]
238. curious(X0) [subsumption resolution 103,123]
242. ~creative(alice) [subsumption resolution 107,238]
263. $false [subsumption resolution 119,242]
% SZS output end Proof for 8718588814050403256659536
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.032 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not quiet or not generous is both generous and curious.
If someone is tall then someone is both humble and wise and vice versa.
Everyone who is not creative or brave is both not curious and not strong and vice versa.
If lucy is either happy or brave then mary is generous or not rich.
If someone is not humble or not quiet then mary is either not patient or strong.
Everyone who is curious or funny is either not happy or not creative.
Everyone who is either not wise or not quiet is both old and creative.
If mary is curious or not quiet then someone is either not curious or funny and vice versa.
Everyone who is humble is either calm or not humble and vice versa.
Everyone who is not humble or patient is curious.
Everyone who is either humble or happy is both brave and patient and vice versa.
Everyone who is not happy is either not happy or brave and vice versa.
If lucy is both not rich and not patient then fred is both not tall and not old and vice versa.
Everyone who is both creative and not rich is both not happy and rich and vice versa.
Everyone who is not generous is generous.
Fred is not curious or wise.
Someone is both not brave and kind.
Someone is not tall. | Lucy is quiet. | entailment | (![X]:((~quiet(X)<~>~generous(X))=>(generous(X)&curious(X))))&
((?[X]:(tall(X)))<=>(?[X]:((humble(X)&wise(X)))))&
(![X]:((~creative(X)|brave(X))<=>(~curious(X)&~strong(X))))&
(((happy(lucy)<~>brave(lucy)))=>((generous(mary)|~rich(mary))))&
((?[X]:((~humble(X)|~quiet(X))))=>((~patient(mary)<~>strong(mary))))&
(![X]:((curious(X)|funny(X))=>(~happy(X)<~>~creative(X))))&
(![X]:((~wise(X)<~>~quiet(X))=>(old(X)&creative(X))))&
(((curious(mary)|~quiet(mary)))<=>(?[X]:((~curious(X)<~>funny(X)))))&
(![X]:(humble(X)<=>(calm(X)<~>~humble(X))))&
(![X]:((~humble(X)|patient(X))=>curious(X)))&
(![X]:((humble(X)<~>happy(X))<=>(brave(X)&patient(X))))&
(![X]:(~happy(X)<=>(~happy(X)<~>brave(X))))&
(((~rich(lucy)&~patient(lucy)))<=>((~tall(fred)&~old(fred))))&
(![X]:((creative(X)&~rich(X))<=>(~happy(X)&rich(X))))&
(![X]:(~generous(X)=>generous(X)))&
((~curious(fred)|wise(fred)))&
(?[X]:((~brave(X)&kind(X))))&
(?[X]:(~tall(X))) | quiet(lucy) | [
"p0",
"p2",
"p5",
"p7",
"p13",
"p14",
"hypothesis"
] | % SZS status Unsatisfiable for 737806453700797270925856
% SZS output start Proof for 737806453700797270925856
1. ! [X0] : ((~quiet(X0) <~> ~generous(X0)) => (curious(X0) & generous(X0))) [input p0]
3. ! [X0] : ((brave(X0) | ~creative(X0)) <=> (~strong(X0) & ~curious(X0))) [input p2]
6. ! [X0] : ((funny(X0) | curious(X0)) => (~happy(X0) <~> ~creative(X0))) [input p5]
8. (~quiet(mary) | curious(mary)) <=> ? [X0] : (~curious(X0) <~> funny(X0)) [input p7]
14. ! [X0] : ((~rich(X0) & creative(X0)) <=> (rich(X0) & ~happy(X0))) [input p13]
15. ! [X0] : (~generous(X0) => generous(X0)) [input p14]
19. ~quiet(lucy) [input hypothesis]
22. ! [X0] : ((curious(X0) & generous(X0)) | (~quiet(X0) <=> ~generous(X0))) [ennf transformation 1]
26. ! [X0] : ((~happy(X0) <~> ~creative(X0)) | (~funny(X0) & ~curious(X0))) [ennf transformation 6]
29. ! [X0] : (generous(X0) | generous(X0)) [ennf transformation 15]
30. ! [X0] : ((curious(X0) & generous(X0)) | ((~quiet(X0) | generous(X0)) & (~generous(X0) | quiet(X0)))) [nnf transformation 22]
36. ! [X0] : (((brave(X0) | ~creative(X0)) | (strong(X0) | curious(X0))) & ((~strong(X0) & ~curious(X0)) | (~brave(X0) & creative(X0)))) [nnf transformation 3]
37. ! [X0] : ((brave(X0) | ~creative(X0) | strong(X0) | curious(X0)) & ((~strong(X0) & ~curious(X0)) | (~brave(X0) & creative(X0)))) [flattening 36]
40. ! [X0] : (((creative(X0) | happy(X0)) & (~creative(X0) | ~happy(X0))) | (~funny(X0) & ~curious(X0))) [nnf transformation 26]
42. ((~quiet(mary) | curious(mary)) | ! [X0] : ((~curious(X0) | ~funny(X0)) & (funny(X0) | curious(X0)))) & (? [X0] : ((~funny(X0) | curious(X0)) & (funny(X0) | ~curious(X0))) | (quiet(mary) & ~curious(mary))) [nnf transformation 8]
43. (~quiet(mary) | curious(mary) | ! [X0] : ((~curious(X0) | ~funny(X0)) & (funny(X0) | curious(X0)))) & (? [X0] : ((~funny(X0) | curious(X0)) & (funny(X0) | ~curious(X0))) | (quiet(mary) & ~curious(mary))) [flattening 42]
44. (~quiet(mary) | curious(mary) | ! [X0] : ((~curious(X0) | ~funny(X0)) & (funny(X0) | curious(X0)))) & (? [X1] : ((~funny(X1) | curious(X1)) & (funny(X1) | ~curious(X1))) | (quiet(mary) & ~curious(mary))) [rectify 43]
45. ? [X1] : ((~funny(X1) | curious(X1)) & (funny(X1) | ~curious(X1))) => ((~funny(sK2) | curious(sK2)) & (funny(sK2) | ~curious(sK2))) [choice axiom]
46. (~quiet(mary) | curious(mary) | ! [X0] : ((~curious(X0) | ~funny(X0)) & (funny(X0) | curious(X0)))) & (((~funny(sK2) | curious(sK2)) & (funny(sK2) | ~curious(sK2))) | (quiet(mary) & ~curious(mary))) [skolemisation 44,45]
53. ! [X0] : (((~rich(X0) & creative(X0)) | (~rich(X0) | happy(X0))) & ((rich(X0) & ~happy(X0)) | (rich(X0) | ~creative(X0)))) [nnf transformation 14]
54. ! [X0] : (((~rich(X0) & creative(X0)) | ~rich(X0) | happy(X0)) & ((rich(X0) & ~happy(X0)) | rich(X0) | ~creative(X0))) [flattening 53]
61. ~generous(X0) | curious(X0) | quiet(X0) [cnf transformation 30]
66. ~curious(X0) | creative(X0) [cnf transformation 37]
77. ~creative(X0) | ~happy(X0) | ~curious(X0) [cnf transformation 40]
80. ~funny(X0) | happy(X0) | creative(X0) [cnf transformation 40]
89. ~quiet(mary) | curious(mary) | funny(X0) | curious(X0) [cnf transformation 46]
112. rich(X0) | rich(X0) | ~creative(X0) [cnf transformation 54]
114. ~rich(X0) | ~rich(X0) | happy(X0) [cnf transformation 54]
115. generous(X0) | generous(X0) [cnf transformation 29]
119. ~quiet(lucy) [cnf transformation 19]
120. generous(X0) [duplicate literal removal 115]
121. ~creative(X0) | rich(X0) [duplicate literal removal 112]
122. ~rich(X0) | happy(X0) [duplicate literal removal 114]
154. 7 <=> happy(lucy) [avatar definition]
155. ~happy(lucy) <- (~7) [avatar component clause 154]
156. happy(lucy) <- (7) [avatar component clause 154]
162. 9 <=> rich(mary) [avatar definition]
163. rich(mary) <- (9) [avatar component clause 162]
185. ~happy(X0) | ~curious(X0) [subsumption resolution 77,66]
190. 15 <=> curious(mary) [avatar definition]
191. ~curious(mary) <- (~15) [avatar component clause 190]
192. curious(mary) <- (15) [avatar component clause 190]
194. 16 <=> quiet(mary) [avatar definition]
196. ~quiet(mary) <- (~16) [avatar component clause 194]
199. 17 <=> ! [X0] : (funny(X0) | curious(X0)) [avatar definition]
200. funny(X0) | curious(X0) <- (17) [avatar component clause 199]
201. 17 | 15 | ~16 [avatar split clause 89,194,190,199]
230. 23 <=> rich(lucy) [avatar definition]
231. rich(lucy) <- (23) [avatar component clause 230]
232. ~rich(lucy) <- (~23) [avatar component clause 230]
247. curious(X0) | quiet(X0) [resolution 61,120]
249. quiet(mary) <- (~15) [resolution 247,191]
252. $false <- (~15, ~16) [subsumption resolution 249,196]
253. 15 | 16 [avatar contradiction clause 252]
254. creative(mary) <- (15) [resolution 192,66]
255. rich(mary) <- (15) [resolution 254,121]
258. 9 | ~15 [avatar split clause 255,190,162]
259. happy(mary) <- (9) [resolution 163,122]
260. ~curious(mary) <- (9) [resolution 259,185]
264. ~15 | ~9 [avatar split clause 260,162,190]
279. happy(X0) | creative(X0) | curious(X0) <- (17) [resolution 80,200]
280. happy(X0) | creative(X0) <- (17) [subsumption resolution 279,66]
397. creative(lucy) <- (~7, 17) [resolution 280,155]
406. rich(lucy) <- (~7, 17) [resolution 397,121]
407. $false <- (~7, 17, ~23) [subsumption resolution 406,232]
408. 7 | ~17 | 23 [avatar contradiction clause 407]
412. ~curious(lucy) <- (7) [resolution 156,185]
415. quiet(lucy) <- (7) [resolution 412,247]
416. $false <- (7) [subsumption resolution 415,119]
417. ~7 [avatar contradiction clause 416]
420. happy(lucy) <- (23) [resolution 231,122]
421. $false <- (~7, 23) [subsumption resolution 420,155]
422. 7 | ~23 [avatar contradiction clause 421]
423. $false [avatar sat refutation 201,253,258,264,408,417,422]
% SZS output end Proof for 737806453700797270925856
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not generous is either not creative or not funny and vice versa.
Everyone who is generous or happy is tall and vice versa.
If someone is either not tall or not creative then mary is both rich and not wise.
Everyone who is not humble is either happy or strong and vice versa.
If someone is both creative and not old then someone is either wise or generous and vice versa.
Everyone who is both curious and not curious is both rich and quiet and vice versa.
If mary is humble or happy then alice is not patient or not strong.
If alice is both calm and not kind then mary is not wise or creative and vice versa.
Everyone who is kind or not humble is rich and vice versa.
If paul is either kind or not strong then someone is rich or patient and vice versa.
Everyone who is not strong is not curious and vice versa.
If someone is either not brave or not curious then someone is either tall or happy and vice versa.
If someone is both not happy and brave then someone is rich or happy and vice versa.
Everyone who is either wise or kind is generous and vice versa.
Everyone who is both not old and not funny is not generous or humble and vice versa.
Everyone who is rich is not creative and vice versa.
Paul is generous.
Fred is happy or not funny.
Lucy is either generous or not humble.
Lucy is both not wise and not patient.
John is wise or happy.
Someone is not funny.
Someone is not happy or calm.
Alice is not wise. | Paul is not rich. | contradiction | (![X]:(~generous(X)<=>(~creative(X)<~>~funny(X))))&
(![X]:((generous(X)|happy(X))<=>tall(X)))&
((?[X]:((~tall(X)<~>~creative(X))))=>((rich(mary)&~wise(mary))))&
(![X]:(~humble(X)<=>(happy(X)<~>strong(X))))&
((?[X]:((creative(X)&~old(X))))<=>(?[X]:((wise(X)<~>generous(X)))))&
(![X]:((curious(X)&~curious(X))<=>(rich(X)&quiet(X))))&
(((humble(mary)|happy(mary)))=>((~patient(alice)|~strong(alice))))&
(((calm(alice)&~kind(alice)))<=>((~wise(mary)|creative(mary))))&
(![X]:((kind(X)|~humble(X))<=>rich(X)))&
(((kind(paul)<~>~strong(paul)))<=>(?[X]:((rich(X)|patient(X)))))&
(![X]:(~strong(X)<=>~curious(X)))&
((?[X]:((~brave(X)<~>~curious(X))))<=>(?[X]:((tall(X)<~>happy(X)))))&
((?[X]:((~happy(X)&brave(X))))<=>(?[X]:((rich(X)|happy(X)))))&
(![X]:((wise(X)<~>kind(X))<=>generous(X)))&
(![X]:((~old(X)&~funny(X))<=>(~generous(X)|humble(X))))&
(![X]:(rich(X)<=>~creative(X)))&
(generous(paul))&
((happy(fred)|~funny(fred)))&
((generous(lucy)<~>~humble(lucy)))&
((~wise(lucy)&~patient(lucy)))&
((wise(john)|happy(john)))&
(?[X]:(~funny(X)))&
(?[X]:((~happy(X)|calm(X))))&
(~wise(alice)) | ~rich(paul) | [
"p0",
"p8",
"p14",
"p15",
"p16",
"hypothesis"
] | % SZS status Unsatisfiable for 4430363616811551869906700
% SZS output start Proof for 4430363616811551869906700
1. ! [X0] : (~generous(X0) <=> (~creative(X0) <~> ~funny(X0))) [input p0]
9. ! [X0] : ((~humble(X0) | kind(X0)) <=> rich(X0)) [input p8]
15. ! [X0] : ((~funny(X0) & ~old(X0)) <=> (humble(X0) | ~generous(X0))) [input p14]
16. ! [X0] : (rich(X0) <=> ~creative(X0)) [input p15]
17. generous(paul) [input p16]
25. ~rich(paul) [input hypothesis]
32. ! [X0] : ((~generous(X0) | ((~creative(X0) | funny(X0)) & (~funny(X0) | creative(X0)))) & (((funny(X0) | creative(X0)) & (~funny(X0) | ~creative(X0))) | generous(X0))) [nnf transformation 1]
46. ! [X0] : (((~humble(X0) | kind(X0)) | ~rich(X0)) & (rich(X0) | (humble(X0) & ~kind(X0)))) [nnf transformation 9]
47. ! [X0] : ((~humble(X0) | kind(X0) | ~rich(X0)) & (rich(X0) | (humble(X0) & ~kind(X0)))) [flattening 46]
64. ! [X0] : (((~funny(X0) & ~old(X0)) | (~humble(X0) & generous(X0))) & ((humble(X0) | ~generous(X0)) | (funny(X0) | old(X0)))) [nnf transformation 15]
65. ! [X0] : (((~funny(X0) & ~old(X0)) | (~humble(X0) & generous(X0))) & (humble(X0) | ~generous(X0) | funny(X0) | old(X0))) [flattening 64]
66. ! [X0] : ((rich(X0) | creative(X0)) & (~creative(X0) | ~rich(X0))) [nnf transformation 16]
75. ~creative(X0) | ~generous(X0) | funny(X0) [cnf transformation 32]
105. humble(X0) | rich(X0) [cnf transformation 47]
136. ~humble(X0) | ~funny(X0) [cnf transformation 65]
138. rich(X0) | creative(X0) [cnf transformation 66]
139. generous(paul) [cnf transformation 17]
149. ~rich(paul) [cnf transformation 25]
377. creative(paul) [resolution 138,149]
453. ~generous(paul) | funny(paul) [resolution 75,377]
457. funny(paul) [subsumption resolution 453,139]
494. 54 <=> humble(paul) [avatar definition]
495. ~humble(paul) <- (~54) [avatar component clause 494]
496. humble(paul) <- (54) [avatar component clause 494]
515. ~funny(paul) <- (54) [resolution 496,136]
518. $false <- (54) [subsumption resolution 515,457]
519. ~54 [avatar contradiction clause 518]
520. rich(paul) <- (~54) [resolution 495,105]
521. $false <- (~54) [subsumption resolution 520,149]
522. 54 [avatar contradiction clause 521]
523. $false [avatar sat refutation 519,522]
% SZS output end Proof for 4430363616811551869906700
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.031 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either tall or happy is both not strong and not happy and vice versa.
If someone is not funny then fred is both not strong and not rich.
If someone is happy or not funny then susan is wise or calm.
Everyone who is funny or not curious is both not creative and kind.
Everyone who is funny or curious is both not strong and not wise and vice versa.
If lucy is both wise and calm then fred is strong and vice versa.
Everyone who is both not funny and not old is either curious or not old and vice versa.
If someone is both not brave and not kind then someone is not happy or brave.
If john is kind then mary is not tall.
Everyone who is not generous or not patient is wise or not rich.
Everyone who is either brave or tall is curious or creative and vice versa.
If mary is either not happy or not brave then mary is quiet or not strong and vice versa.
Everyone who is not happy or not funny is either calm or not rich.
Everyone who is both tall and funny is both not wise and old.
Someone is both not brave and not quiet.
Lucy is both tall and not wise.
Someone is both patient and not generous.
Someone is not tall or funny.
Someone is calm.
Someone is calm or old.
Someone is patient. | Mary is curious. | contradiction | (![X]:((tall(X)<~>happy(X))<=>(~strong(X)&~happy(X))))&
((?[X]:(~funny(X)))=>((~strong(fred)&~rich(fred))))&
((?[X]:((happy(X)|~funny(X))))=>((wise(susan)|calm(susan))))&
(![X]:((funny(X)|~curious(X))=>(~creative(X)&kind(X))))&
(![X]:((funny(X)|curious(X))<=>(~strong(X)&~wise(X))))&
(((wise(lucy)&calm(lucy)))<=>(strong(fred)))&
(![X]:((~funny(X)&~old(X))<=>(curious(X)<~>~old(X))))&
((?[X]:((~brave(X)&~kind(X))))=>(?[X]:((~happy(X)|brave(X)))))&
((kind(john))=>(~tall(mary)))&
(![X]:((~generous(X)|~patient(X))=>(wise(X)|~rich(X))))&
(![X]:((brave(X)<~>tall(X))<=>(curious(X)|creative(X))))&
(((~happy(mary)<~>~brave(mary)))<=>((quiet(mary)|~strong(mary))))&
(![X]:((~happy(X)|~funny(X))=>(calm(X)<~>~rich(X))))&
(![X]:((tall(X)&funny(X))=>(~wise(X)&old(X))))&
(?[X]:((~brave(X)&~quiet(X))))&
((tall(lucy)&~wise(lucy)))&
(?[X]:((patient(X)&~generous(X))))&
(?[X]:((~tall(X)|funny(X))))&
(?[X]:(calm(X)))&
(?[X]:((calm(X)|old(X))))&
(?[X]:(patient(X))) | curious(mary) | [
"p0",
"p3",
"p4",
"p6",
"p8",
"hypothesis"
] | % SZS status Unsatisfiable for 9059098933199665796726362
% SZS output start Proof for 9059098933199665796726362
1. ! [X0] : ((tall(X0) <~> happy(X0)) <=> (~happy(X0) & ~strong(X0))) [input p0]
4. ! [X0] : ((~curious(X0) | funny(X0)) => (kind(X0) & ~creative(X0))) [input p3]
5. ! [X0] : ((curious(X0) | funny(X0)) <=> (~wise(X0) & ~strong(X0))) [input p4]
7. ! [X0] : ((~old(X0) & ~funny(X0)) <=> (curious(X0) <~> ~old(X0))) [input p6]
9. kind(john) => ~tall(mary) [input p8]
22. curious(mary) [input hypothesis]
30. ! [X0] : ((kind(X0) & ~creative(X0)) | (curious(X0) & ~funny(X0))) [ennf transformation 4]
32. ~tall(mary) | ~kind(john) [ennf transformation 9]
38. ! [X0] : ((((~happy(X0) | ~tall(X0)) & (happy(X0) | tall(X0))) | (happy(X0) | strong(X0))) & ((~happy(X0) & ~strong(X0)) | ((tall(X0) | ~happy(X0)) & (happy(X0) | ~tall(X0))))) [nnf transformation 1]
39. ! [X0] : ((((~happy(X0) | ~tall(X0)) & (happy(X0) | tall(X0))) | happy(X0) | strong(X0)) & ((~happy(X0) & ~strong(X0)) | ((tall(X0) | ~happy(X0)) & (happy(X0) | ~tall(X0))))) [flattening 38]
40. ! [X0] : (((curious(X0) | funny(X0)) | (wise(X0) | strong(X0))) & ((~wise(X0) & ~strong(X0)) | (~curious(X0) & ~funny(X0)))) [nnf transformation 5]
41. ! [X0] : ((curious(X0) | funny(X0) | wise(X0) | strong(X0)) & ((~wise(X0) & ~strong(X0)) | (~curious(X0) & ~funny(X0)))) [flattening 40]
44. ! [X0] : (((~old(X0) & ~funny(X0)) | ((curious(X0) | old(X0)) & (~old(X0) | ~curious(X0)))) & (((old(X0) | ~curious(X0)) & (~old(X0) | curious(X0))) | (old(X0) | funny(X0)))) [nnf transformation 7]
45. ! [X0] : (((~old(X0) & ~funny(X0)) | ((curious(X0) | old(X0)) & (~old(X0) | ~curious(X0)))) & (((old(X0) | ~curious(X0)) & (~old(X0) | curious(X0))) | old(X0) | funny(X0))) [flattening 44]
67. ~happy(X0) | tall(X0) | ~happy(X0) [cnf transformation 39]
68. happy(X0) | tall(X0) | happy(X0) | strong(X0) [cnf transformation 39]
76. ~funny(X0) | kind(X0) [cnf transformation 30]
77. kind(X0) | curious(X0) [cnf transformation 30]
79. ~curious(X0) | ~strong(X0) [cnf transformation 41]
87. old(X0) | ~curious(X0) | old(X0) | funny(X0) [cnf transformation 45]
90. ~old(X0) | ~old(X0) | ~curious(X0) [cnf transformation 45]
93. ~tall(mary) | ~kind(john) [cnf transformation 32]
121. curious(mary) [cnf transformation 22]
122. old(X0) | ~curious(X0) | funny(X0) [duplicate literal removal 87]
123. ~old(X0) | ~curious(X0) [duplicate literal removal 90]
124. ~happy(X0) | tall(X0) [duplicate literal removal 67]
125. strong(X0) | tall(X0) | happy(X0) [duplicate literal removal 68]
163. ~curious(X0) | funny(X0) [subsumption resolution 122,123]
177. 12 <=> kind(john) [avatar definition]
179. ~kind(john) <- (~12) [avatar component clause 177]
181. 13 <=> tall(mary) [avatar definition]
183. ~tall(mary) <- (~13) [avatar component clause 181]
184. ~12 | ~13 [avatar split clause 93,181,177]
188. 14 <=> strong(mary) [avatar definition]
189. ~strong(mary) <- (~14) [avatar component clause 188]
192. 15 <=> happy(mary) [avatar definition]
193. ~happy(mary) <- (~15) [avatar component clause 192]
194. happy(mary) <- (15) [avatar component clause 192]
228. curious(john) <- (~12) [resolution 77,179]
229. ~strong(mary) [resolution 79,121]
233. ~14 [avatar split clause 229,188]
237. tall(mary) <- (15) [resolution 124,194]
238. 13 | ~15 [avatar split clause 237,192,181]
240. funny(john) <- (~12) [resolution 163,228]
246. kind(john) <- (~12) [resolution 240,76]
247. $false <- (~12) [subsumption resolution 246,179]
248. 12 [avatar contradiction clause 247]
295. tall(mary) | happy(mary) <- (~14) [resolution 125,189]
298. happy(mary) <- (~13, ~14) [subsumption resolution 295,183]
299. $false <- (~13, ~14, ~15) [subsumption resolution 298,193]
300. 13 | 14 | 15 [avatar contradiction clause 299]
301. $false [avatar sat refutation 184,233,238,248,300]
% SZS output end Proof for 9059098933199665796726362
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.037 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is both old and creative is both not strong and kind.
Everyone who is both curious and generous is not quiet.
If someone is wise or not humble then paul is both not funny and happy.
If someone is both creative and quiet then lucy is wise or not curious and vice versa.
Everyone who is either not funny or wise is wise or not rich.
If john is not brave then fred is happy or strong and vice versa.
If fred is not strong then paul is either curious or happy and vice versa.
Everyone who is creative or old is wise.
Everyone who is not brave or tall is either happy or patient.
Everyone who is not brave or curious is both creative and strong.
Everyone who is creative or kind is old or not funny and vice versa.
If someone is either not curious or wise then someone is not quiet and vice versa.
If someone is both not patient and not curious then someone is either strong or old.
If susan is not patient then john is either not rich or not funny and vice versa.
Everyone who is both not brave and quiet is not funny.
If someone is both wise and calm then someone is not curious or kind.
Alice is wise.
Lucy is either not quiet or not wise.
Someone is calm or not rich.
Someone is both quiet and not patient.
Someone is quiet or tall.
Someone is both generous and not quiet.
Someone is old or patient.
John is either strong or creative. | Paul is curious. | contradiction | (![X]:((old(X)&creative(X))=>(~strong(X)&kind(X))))&
(![X]:((curious(X)&generous(X))=>~quiet(X)))&
((?[X]:((wise(X)|~humble(X))))=>((~funny(paul)&happy(paul))))&
((?[X]:((creative(X)&quiet(X))))<=>((wise(lucy)|~curious(lucy))))&
(![X]:((~funny(X)<~>wise(X))=>(wise(X)|~rich(X))))&
((~brave(john))<=>((happy(fred)|strong(fred))))&
((~strong(fred))<=>((curious(paul)<~>happy(paul))))&
(![X]:((creative(X)|old(X))=>wise(X)))&
(![X]:((~brave(X)|tall(X))=>(happy(X)<~>patient(X))))&
(![X]:((~brave(X)|curious(X))=>(creative(X)&strong(X))))&
(![X]:((creative(X)|kind(X))<=>(old(X)|~funny(X))))&
((?[X]:((~curious(X)<~>wise(X))))<=>(?[X]:(~quiet(X))))&
((?[X]:((~patient(X)&~curious(X))))=>(?[X]:((strong(X)<~>old(X)))))&
((~patient(susan))<=>((~rich(john)<~>~funny(john))))&
(![X]:((~brave(X)&quiet(X))=>~funny(X)))&
((?[X]:((wise(X)&calm(X))))=>(?[X]:((~curious(X)|kind(X)))))&
(wise(alice))&
((~quiet(lucy)<~>~wise(lucy)))&
(?[X]:((calm(X)|~rich(X))))&
(?[X]:((quiet(X)&~patient(X))))&
(?[X]:((quiet(X)|tall(X))))&
(?[X]:((generous(X)&~quiet(X))))&
(?[X]:((old(X)|patient(X))))&
((strong(john)<~>creative(john))) | curious(paul) | [
"p2",
"p5",
"p6",
"p9",
"p16",
"p23",
"hypothesis"
] | % SZS status Unsatisfiable for 439885402391886288838477
% SZS output start Proof for 439885402391886288838477
3. ? [X0] : (~humble(X0) | wise(X0)) => (happy(paul) & ~funny(paul)) [input p2]
6. ~brave(john) <=> (strong(fred) | happy(fred)) [input p5]
7. ~strong(fred) <=> (curious(paul) <~> happy(paul)) [input p6]
10. ! [X0] : ((curious(X0) | ~brave(X0)) => (strong(X0) & creative(X0))) [input p9]
17. wise(alice) [input p16]
24. strong(john) <~> creative(john) [input p23]
25. curious(paul) [input hypothesis]
29. ? [X0] : wise(X0) => (happy(paul) & ~funny(paul)) [pure predicate removal 3]
34. (happy(paul) & ~funny(paul)) | ! [X0] : ~wise(X0) [ennf transformation 29]
39. ! [X0] : ((strong(X0) & creative(X0)) | (~curious(X0) & brave(X0))) [ennf transformation 10]
50. (~brave(john) | (~strong(fred) & ~happy(fred))) & ((strong(fred) | happy(fred)) | brave(john)) [nnf transformation 6]
51. (~brave(john) | (~strong(fred) & ~happy(fred))) & (strong(fred) | happy(fred) | brave(john)) [flattening 50]
52. (~strong(fred) | ((curious(paul) | ~happy(paul)) & (happy(paul) | ~curious(paul)))) & (((~happy(paul) | ~curious(paul)) & (happy(paul) | curious(paul))) | strong(fred)) [nnf transformation 7]
80. (~creative(john) | ~strong(john)) & (creative(john) | strong(john)) [nnf transformation 24]
85. happy(paul) | ~wise(X0) [cnf transformation 34]
95. ~brave(john) | ~strong(fred) [cnf transformation 51]
97. ~happy(paul) | ~curious(paul) | strong(fred) [cnf transformation 52]
106. brave(X0) | creative(X0) [cnf transformation 39]
108. brave(X0) | strong(X0) [cnf transformation 39]
126. wise(alice) [cnf transformation 17]
137. ~creative(john) | ~strong(john) [cnf transformation 80]
138. curious(paul) [cnf transformation 25]
141. 1 <=> ! [X0] : ~wise(X0) [avatar definition]
142. ~wise(X0) <- (1) [avatar component clause 141]
144. 2 <=> happy(paul) [avatar definition]
147. 1 | 2 [avatar split clause 85,144,141]
178. 9 <=> strong(fred) [avatar definition]
182. 10 <=> brave(john) [avatar definition]
184. ~brave(john) <- (~10) [avatar component clause 182]
185. ~9 | ~10 [avatar split clause 95,182,178]
193. 12 <=> curious(paul) [avatar definition]
198. 9 | ~12 | ~2 [avatar split clause 97,144,193,178]
301. 35 <=> strong(john) [avatar definition]
303. ~strong(john) <- (~35) [avatar component clause 301]
305. 36 <=> creative(john) [avatar definition]
308. ~35 | ~36 [avatar split clause 137,305,301]
310. 12 [avatar split clause 138,193]
313. creative(john) <- (~10) [resolution 106,184]
316. 36 | 10 [avatar split clause 313,182,305]
319. strong(john) <- (~10) [resolution 108,184]
320. $false <- (~10, ~35) [subsumption resolution 319,303]
321. 10 | 35 [avatar contradiction clause 320]
323. $false <- (1) [resolution 142,126]
328. ~1 [avatar contradiction clause 323]
330. $false [avatar sat refutation 147,185,198,308,310,316,321,328]
% SZS output end Proof for 439885402391886288838477
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.036 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not creative or generous is not wise or rich and vice versa. Everyone who is not funny or wise is either not creative or not strong and vice versa. Everyone who is both calm and not wise is either kind or not generous and vice versa. If fred is not wise or not patient then john is both wise and not tall and vice versa. Everyone who is both calm and not old is not brave or old and vice versa. If someone is wise or curious then alice is both humble and kind. If someone is not funny then someone is either strong or generous. Everyone who is either creative or patient is not old and vice versa. If someone is tall then someone is both rich and quiet. Everyone who is not quiet is humble and vice versa. If lucy is brave or not rich then someone is both generous and quiet and vice versa. Everyone who is not calm is either not strong or not humble. If lucy is both not quiet and generous then someone is either not brave or strong and vice versa. Everyone who is calm or not calm is not curious. Everyone who is both kind and calm is not calm or creative. Everyone who is patient or curious is both not funny and not happy and vice versa. Someone is both strong and not generous. Someone is not wise or old. Someone is either strong or rich. Someone is happy or not wise. Susan is strong. | Fred is not creative. | neutral | (![X]:((~creative(X)|generous(X))<=>(~wise(X)|rich(X))))&
(![X]:((~funny(X)|wise(X))<=>(~creative(X)<~>~strong(X))))&
(![X]:((calm(X)&~wise(X))<=>(kind(X)<~>~generous(X))))&
(((~wise(fred)|~patient(fred)))<=>((wise(john)&~tall(john))))&
(![X]:((calm(X)&~old(X))<=>(~brave(X)|old(X))))&
((?[X]:((wise(X)|curious(X))))=>((humble(alice)&kind(alice))))&
((?[X]:(~funny(X)))=>(?[X]:((strong(X)<~>generous(X)))))&
(![X]:((creative(X)<~>patient(X))<=>~old(X)))&
((?[X]:(tall(X)))=>(?[X]:((rich(X)&quiet(X)))))&
(![X]:(~quiet(X)<=>humble(X)))&
(((brave(lucy)|~rich(lucy)))<=>(?[X]:((generous(X)&quiet(X)))))&
(![X]:(~calm(X)=>(~strong(X)<~>~humble(X))))&
(((~quiet(lucy)&generous(lucy)))<=>(?[X]:((~brave(X)<~>strong(X)))))&
(![X]:((calm(X)|~calm(X))=>~curious(X)))&
(![X]:((kind(X)&calm(X))=>(~calm(X)|creative(X))))&
(![X]:((patient(X)|curious(X))<=>(~funny(X)&~happy(X))))&
(?[X]:((strong(X)&~generous(X))))&
(?[X]:((~wise(X)|old(X))))&
(?[X]:((strong(X)<~>rich(X))))&
(?[X]:((happy(X)|~wise(X))))&
(strong(susan)) | ~creative(fred) | [] | null | 0 |
If someone is both creative and happy then susan is not generous.
Everyone who is not brave or humble is humble.
If paul is funny then fred is both brave and not patient and vice versa.
Everyone who is either not old or not humble is both not curious and rich and vice versa.
Everyone who is both not tall and generous is not patient or not humble.
If paul is not old or not curious then mary is not happy and vice versa.
Everyone who is both not humble and quiet is both not strong and not kind and vice versa.
Everyone who is happy is either not quiet or not patient and vice versa.
Everyone who is not rich or creative is creative or rich.
Everyone who is curious or rich is not rich or not calm and vice versa.
Everyone who is both happy and not curious is wise or kind and vice versa.
If susan is not brave then fred is either curious or not humble.
Everyone who is either not kind or curious is either calm or not creative and vice versa.
If john is either not funny or not rich then lucy is not wise or patient and vice versa.
Everyone who is not happy or kind is old or not patient and vice versa.
If alice is calm then someone is either creative or not humble and vice versa.
Someone is either not happy or not kind.
Someone is both not calm and old.
Alice is either not creative or not patient.
John is strong or curious. | Mary is not wise. | entailment | ((?[X]:((creative(X)&happy(X))))=>(~generous(susan)))&
(![X]:((~brave(X)|humble(X))=>humble(X)))&
((funny(paul))<=>((brave(fred)&~patient(fred))))&
(![X]:((~old(X)<~>~humble(X))<=>(~curious(X)&rich(X))))&
(![X]:((~tall(X)&generous(X))=>(~patient(X)|~humble(X))))&
(((~old(paul)|~curious(paul)))<=>(~happy(mary)))&
(![X]:((~humble(X)&quiet(X))<=>(~strong(X)&~kind(X))))&
(![X]:(happy(X)<=>(~quiet(X)<~>~patient(X))))&
(![X]:((~rich(X)|creative(X))=>(creative(X)|rich(X))))&
(![X]:((curious(X)|rich(X))<=>(~rich(X)|~calm(X))))&
(![X]:((happy(X)&~curious(X))<=>(wise(X)|kind(X))))&
((~brave(susan))=>((curious(fred)<~>~humble(fred))))&
(![X]:((~kind(X)<~>curious(X))<=>(calm(X)<~>~creative(X))))&
(((~funny(john)<~>~rich(john)))<=>((~wise(lucy)|patient(lucy))))&
(![X]:((~happy(X)|kind(X))<=>(old(X)|~patient(X))))&
((calm(alice))<=>(?[X]:((creative(X)<~>~humble(X)))))&
(?[X]:((~happy(X)<~>~kind(X))))&
(?[X]:((~calm(X)&old(X))))&
((~creative(alice)<~>~patient(alice)))&
((strong(john)|curious(john))) | ~wise(mary) | [
"p3",
"p5",
"p8",
"p9",
"p10",
"p12",
"p15",
"hypothesis"
] | % SZS status Unsatisfiable for 7619366959523729586216968
% SZS output start Proof for 7619366959523729586216968
4. ! [X0] : ((~old(X0) <~> ~humble(X0)) <=> (rich(X0) & ~curious(X0))) [input p3]
6. (~curious(paul) | ~old(paul)) <=> ~happy(mary) [input p5]
9. ! [X0] : ((creative(X0) | ~rich(X0)) => (rich(X0) | creative(X0))) [input p8]
10. ! [X0] : ((rich(X0) | curious(X0)) <=> (~calm(X0) | ~rich(X0))) [input p9]
11. ! [X0] : ((~curious(X0) & happy(X0)) <=> (kind(X0) | wise(X0))) [input p10]
13. ! [X0] : ((~kind(X0) <~> curious(X0)) <=> (calm(X0) <~> ~creative(X0))) [input p12]
16. calm(alice) <=> ? [X0] : (creative(X0) <~> ~humble(X0)) [input p15]
21. wise(mary) [input hypothesis]
25. ! [X0] : ((rich(X0) | creative(X0)) | (~creative(X0) & rich(X0))) [ennf transformation 9]
26. ! [X0] : (rich(X0) | creative(X0) | (~creative(X0) & rich(X0))) [flattening 25]
30. ! [X0] : ((((humble(X0) | old(X0)) & (~humble(X0) | ~old(X0))) | (~rich(X0) | curious(X0))) & ((rich(X0) & ~curious(X0)) | ((~old(X0) | humble(X0)) & (~humble(X0) | old(X0))))) [nnf transformation 4]
31. ! [X0] : ((((humble(X0) | old(X0)) & (~humble(X0) | ~old(X0))) | ~rich(X0) | curious(X0)) & ((rich(X0) & ~curious(X0)) | ((~old(X0) | humble(X0)) & (~humble(X0) | old(X0))))) [flattening 30]
32. ((~curious(paul) | ~old(paul)) | happy(mary)) & (~happy(mary) | (curious(paul) & old(paul))) [nnf transformation 6]
33. (~curious(paul) | ~old(paul) | happy(mary)) & (~happy(mary) | (curious(paul) & old(paul))) [flattening 32]
37. ! [X0] : (((rich(X0) | curious(X0)) | (calm(X0) & rich(X0))) & ((~calm(X0) | ~rich(X0)) | (~rich(X0) & ~curious(X0)))) [nnf transformation 10]
38. ! [X0] : ((rich(X0) | curious(X0) | (calm(X0) & rich(X0))) & (~calm(X0) | ~rich(X0) | (~rich(X0) & ~curious(X0)))) [flattening 37]
39. ! [X0] : (((~curious(X0) & happy(X0)) | (~kind(X0) & ~wise(X0))) & ((kind(X0) | wise(X0)) | (curious(X0) | ~happy(X0)))) [nnf transformation 11]
40. ! [X0] : (((~curious(X0) & happy(X0)) | (~kind(X0) & ~wise(X0))) & (kind(X0) | wise(X0) | curious(X0) | ~happy(X0))) [flattening 39]
42. ! [X0] : ((((~curious(X0) | kind(X0)) & (curious(X0) | ~kind(X0))) | ((calm(X0) | creative(X0)) & (~creative(X0) | ~calm(X0)))) & (((creative(X0) | ~calm(X0)) & (~creative(X0) | calm(X0))) | ((~kind(X0) | ~curious(X0)) & (curious(X0) | kind(X0))))) [nnf transformation 13]
47. (calm(alice) | ! [X0] : ((creative(X0) | humble(X0)) & (~humble(X0) | ~creative(X0)))) & (? [X0] : ((humble(X0) | ~creative(X0)) & (~humble(X0) | creative(X0))) | ~calm(alice)) [nnf transformation 16]
48. (calm(alice) | ! [X0] : ((creative(X0) | humble(X0)) & (~humble(X0) | ~creative(X0)))) & (? [X1] : ((humble(X1) | ~creative(X1)) & (~humble(X1) | creative(X1))) | ~calm(alice)) [rectify 47]
49. ? [X1] : ((humble(X1) | ~creative(X1)) & (~humble(X1) | creative(X1))) => ((humble(sK0) | ~creative(sK0)) & (~humble(sK0) | creative(sK0))) [choice axiom]
50. (calm(alice) | ! [X0] : ((creative(X0) | humble(X0)) & (~humble(X0) | ~creative(X0)))) & (((humble(sK0) | ~creative(sK0)) & (~humble(sK0) | creative(sK0))) | ~calm(alice)) [skolemisation 48,49]
63. ~curious(X0) | ~old(X0) | humble(X0) [cnf transformation 31]
68. ~happy(mary) | old(paul) [cnf transformation 33]
69. ~happy(mary) | curious(paul) [cnf transformation 33]
79. rich(X0) | creative(X0) | rich(X0) [cnf transformation 26]
82. ~calm(X0) | ~rich(X0) | ~rich(X0) [cnf transformation 38]
83. rich(X0) | curious(X0) | rich(X0) [cnf transformation 38]
86. ~wise(X0) | happy(X0) [cnf transformation 40]
89. ~kind(X0) | ~curious(X0) [cnf transformation 40]
98. ~curious(X0) | kind(X0) | ~creative(X0) | ~calm(X0) [cnf transformation 42]
99. ~curious(X0) | kind(X0) | calm(X0) | creative(X0) [cnf transformation 42]
112. calm(alice) | ~humble(X0) | ~creative(X0) [cnf transformation 50]
121. wise(mary) [cnf transformation 21]
122. ~calm(X0) | ~rich(X0) [duplicate literal removal 82]
123. rich(X0) | curious(X0) [duplicate literal removal 83]
124. rich(X0) | creative(X0) [duplicate literal removal 79]
141. 4 <=> happy(mary) [avatar definition]
145. 5 <=> old(paul) [avatar definition]
146. old(paul) <- (5) [avatar component clause 145]
149. 6 <=> curious(paul) [avatar definition]
150. curious(paul) <- (6) [avatar component clause 149]
153. 6 | ~4 [avatar split clause 69,141,149]
154. 5 | ~4 [avatar split clause 68,141,145]
169. ~curious(X0) | calm(X0) | creative(X0) [subsumption resolution 99,89]
170. ~calm(X0) | ~creative(X0) | ~curious(X0) [subsumption resolution 98,89]
199. 15 <=> calm(alice) [avatar definition]
201. calm(alice) <- (15) [avatar component clause 199]
204. 16 <=> ! [X0] : (~humble(X0) | ~creative(X0)) [avatar definition]
205. ~humble(X0) | ~creative(X0) <- (16) [avatar component clause 204]
206. 16 | 15 [avatar split clause 112,199,204]
220. 19 <=> creative(alice) [avatar definition]
221. ~creative(alice) <- (~19) [avatar component clause 220]
222. creative(alice) <- (19) [avatar component clause 220]
242. happy(mary) [resolution 86,121]
245. 4 [avatar split clause 242,141]
247. ~rich(alice) <- (15) [resolution 122,201]
250. curious(alice) <- (15) [resolution 247,123]
264. ~old(paul) | humble(paul) <- (6) [resolution 63,150]
266. humble(paul) <- (5, 6) [subsumption resolution 264,146]
379. calm(paul) | creative(paul) <- (6) [resolution 169,150]
382. 42 <=> creative(paul) [avatar definition]
383. ~creative(paul) <- (~42) [avatar component clause 382]
384. creative(paul) <- (42) [avatar component clause 382]
386. 43 <=> calm(paul) [avatar definition]
388. calm(paul) <- (43) [avatar component clause 386]
389. 42 | 43 | ~6 [avatar split clause 379,149,386,382]
390. ~creative(alice) | ~curious(alice) <- (15) [resolution 170,201]
392. ~curious(alice) <- (15, 19) [subsumption resolution 390,222]
393. $false <- (15, 19) [subsumption resolution 392,250]
394. ~15 | ~19 [avatar contradiction clause 393]
428. ~creative(paul) <- (5, 6, 16) [resolution 205,266]
429. $false <- (5, 6, 16, 42) [subsumption resolution 428,384]
430. ~5 | ~6 | ~16 | ~42 [avatar contradiction clause 429]
432. ~rich(alice) <- (15) [resolution 201,122]
439. creative(alice) <- (15) [resolution 432,124]
441. $false <- (15, ~19) [subsumption resolution 439,221]
442. ~15 | 19 [avatar contradiction clause 441]
457. ~rich(paul) <- (43) [resolution 388,122]
591. creative(paul) <- (43) [resolution 457,124]
593. $false <- (~42, 43) [subsumption resolution 591,383]
594. 42 | ~43 [avatar contradiction clause 593]
595. $false [avatar sat refutation 153,154,206,245,389,394,430,442,594]
% SZS output end Proof for 7619366959523729586216968
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5245
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is either not calm or funny is both not generous and not kind and vice versa.
If lucy is not old or not tall then someone is funny or happy.
Everyone who is both not strong and tall is rich and vice versa.
If someone is both not strong and not quiet then someone is brave or not humble.
Everyone who is both quiet and curious is either not generous or not quiet and vice versa.
Everyone who is happy or not brave is not kind.
Everyone who is not funny or kind is not happy and vice versa.
If fred is either curious or not calm then lucy is both not strong and not quiet.
If alice is either happy or calm then susan is both not quiet and quiet.
If john is either humble or not humble then someone is not generous and vice versa.
Everyone who is not old is both funny and not patient.
Everyone who is not kind or not generous is both tall and kind and vice versa.
If someone is either tall or calm then mary is creative or not strong and vice versa.
Everyone who is quiet is not generous or not kind and vice versa.
If someone is either brave or not humble then mary is creative and vice versa.
Everyone who is either old or curious is either calm or curious and vice versa.
Someone is both rich and old.
Alice is not happy or old.
Someone is either generous or brave.
Someone is curious or quiet.
John is both humble and not patient.
Someone is not generous. | John is not happy. | entailment | (![X]:((~calm(X)<~>funny(X))<=>(~generous(X)&~kind(X))))&
(((~old(lucy)|~tall(lucy)))=>(?[X]:((funny(X)|happy(X)))))&
(![X]:((~strong(X)&tall(X))<=>rich(X)))&
((?[X]:((~strong(X)&~quiet(X))))=>(?[X]:((brave(X)|~humble(X)))))&
(![X]:((quiet(X)&curious(X))<=>(~generous(X)<~>~quiet(X))))&
(![X]:((happy(X)|~brave(X))=>~kind(X)))&
(![X]:((~funny(X)|kind(X))<=>~happy(X)))&
(((curious(fred)<~>~calm(fred)))=>((~strong(lucy)&~quiet(lucy))))&
(((happy(alice)<~>calm(alice)))=>((~quiet(susan)&quiet(susan))))&
(((humble(john)<~>~humble(john)))<=>(?[X]:(~generous(X))))&
(![X]:(~old(X)=>(funny(X)&~patient(X))))&
(![X]:((~kind(X)|~generous(X))<=>(tall(X)&kind(X))))&
((?[X]:((tall(X)<~>calm(X))))<=>((creative(mary)|~strong(mary))))&
(![X]:(quiet(X)<=>(~generous(X)|~kind(X))))&
((?[X]:((brave(X)<~>~humble(X))))<=>(creative(mary)))&
(![X]:((old(X)<~>curious(X))<=>(calm(X)<~>curious(X))))&
(?[X]:((rich(X)&old(X))))&
((~happy(alice)|old(alice)))&
(?[X]:((generous(X)<~>brave(X))))&
(?[X]:((curious(X)|quiet(X))))&
((humble(john)&~patient(john)))&
(?[X]:(~generous(X))) | ~happy(john) | [
"p5",
"p11",
"hypothesis"
] | % SZS status Unsatisfiable for 5016116810783417801269135
% SZS output start Proof for 5016116810783417801269135
6. ! [X0] : ((~brave(X0) | happy(X0)) => ~kind(X0)) [input p5]
12. ! [X0] : ((~generous(X0) | ~kind(X0)) <=> (kind(X0) & tall(X0))) [input p11]
23. happy(john) [input hypothesis]
31. ! [X0] : (~kind(X0) | (brave(X0) & ~happy(X0))) [ennf transformation 6]
52. ! [X0] : (((~generous(X0) | ~kind(X0)) | (~kind(X0) | ~tall(X0))) & ((kind(X0) & tall(X0)) | (generous(X0) & kind(X0)))) [nnf transformation 12]
53. ! [X0] : ((~generous(X0) | ~kind(X0) | ~kind(X0) | ~tall(X0)) & ((kind(X0) & tall(X0)) | (generous(X0) & kind(X0)))) [flattening 52]
92. ~happy(X0) | ~kind(X0) [cnf transformation 31]
112. kind(X0) | kind(X0) [cnf transformation 53]
144. happy(john) [cnf transformation 23]
149. kind(X0) [duplicate literal removal 112]
294. ~kind(john) [resolution 92,144]
295. $false [subsumption resolution 294,149]
% SZS output end Proof for 5016116810783417801269135
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.038 s
% ------------------------------
% ------------------------------
| 0 |
Everyone who is not quiet is either not rich or rich.
Everyone who is both wise and kind is patient or not kind.
If fred is not old then fred is both not funny and happy and vice versa.
Everyone who is not happy is either brave or not strong.
If mary is calm then mary is humble.
If someone is not quiet or not generous then someone is generous or not rich.
Everyone who is either humble or wise is tall and vice versa.
Everyone who is rich is either quiet or not strong.
If paul is not wise then paul is tall or not rich and vice versa.
If lucy is both not generous and not creative then susan is not quiet or humble and vice versa.
If alice is both calm and happy then someone is funny or not creative and vice versa.
Everyone who is not generous or not tall is either not strong or generous and vice versa.
Everyone who is not generous is not happy or not patient and vice versa.
If lucy is calm or strong then someone is either not funny or curious and vice versa.
Everyone who is not creative or not rich is both wise and kind and vice versa.
If fred is curious or generous then someone is either not generous or humble and vice versa.
Someone is not generous or humble.
Susan is wise or not rich.
Someone is both not humble and generous.
Someone is either not happy or brave.
Someone is quiet.
Fred is not quiet.
Someone is either wise or not happy. | Fred is not curious. | neutral | (![X]:(~quiet(X)=>(~rich(X)<~>rich(X))))&
(![X]:((wise(X)&kind(X))=>(patient(X)|~kind(X))))&
((~old(fred))<=>((~funny(fred)&happy(fred))))&
(![X]:(~happy(X)=>(brave(X)<~>~strong(X))))&
((calm(mary))=>(humble(mary)))&
((?[X]:((~quiet(X)|~generous(X))))=>(?[X]:((generous(X)|~rich(X)))))&
(![X]:((humble(X)<~>wise(X))<=>tall(X)))&
(![X]:(rich(X)=>(quiet(X)<~>~strong(X))))&
((~wise(paul))<=>((tall(paul)|~rich(paul))))&
(((~generous(lucy)&~creative(lucy)))<=>((~quiet(susan)|humble(susan))))&
(((calm(alice)&happy(alice)))<=>(?[X]:((funny(X)|~creative(X)))))&
(![X]:((~generous(X)|~tall(X))<=>(~strong(X)<~>generous(X))))&
(![X]:(~generous(X)<=>(~happy(X)|~patient(X))))&
(((calm(lucy)|strong(lucy)))<=>(?[X]:((~funny(X)<~>curious(X)))))&
(![X]:((~creative(X)|~rich(X))<=>(wise(X)&kind(X))))&
(((curious(fred)|generous(fred)))<=>(?[X]:((~generous(X)<~>humble(X)))))&
(?[X]:((~generous(X)|humble(X))))&
((wise(susan)|~rich(susan)))&
(?[X]:((~humble(X)&generous(X))))&
(?[X]:((~happy(X)<~>brave(X))))&
(?[X]:(quiet(X)))&
(~quiet(fred))&
(?[X]:((wise(X)<~>~happy(X)))) | ~curious(fred) | [] | null | 0 |
If mary is generous then lucy is not happy or quiet.
Everyone who is creative or patient is either old or generous and vice versa.
Everyone who is either not old or not generous is either not quiet or curious and vice versa.
Everyone who is patient or brave is not happy or not rich.
If alice is not strong or not curious then lucy is patient and vice versa.
If someone is either creative or not wise then someone is kind.
Everyone who is not wise is patient.
If mary is humble then someone is both rich and curious.
If lucy is not tall then alice is curious and vice versa.
Everyone who is happy or brave is either not quiet or not kind.
Everyone who is old is not happy or brave.
Everyone who is happy is either brave or not kind.
Everyone who is generous or kind is both calm and tall.
Everyone who is calm is both patient and tall and vice versa.
Everyone who is not creative or not patient is kind.
Everyone who is quiet or not creative is rich or not strong.
Susan is strong or generous.
Someone is patient or not funny.
Someone is both creative and not strong.
Mary is rich or curious.
John is either humble or tall.
Someone is both not old and not strong.
Someone is not kind.
Fred is either not generous or not wise. | Lucy is not happy. | neutral | ((generous(mary))=>((~happy(lucy)|quiet(lucy))))&
(![X]:((creative(X)|patient(X))<=>(old(X)<~>generous(X))))&
(![X]:((~old(X)<~>~generous(X))<=>(~quiet(X)<~>curious(X))))&
(![X]:((patient(X)|brave(X))=>(~happy(X)|~rich(X))))&
(((~strong(alice)|~curious(alice)))<=>(patient(lucy)))&
((?[X]:((creative(X)<~>~wise(X))))=>(?[X]:(kind(X))))&
(![X]:(~wise(X)=>patient(X)))&
((humble(mary))=>(?[X]:((rich(X)&curious(X)))))&
((~tall(lucy))<=>(curious(alice)))&
(![X]:((happy(X)|brave(X))=>(~quiet(X)<~>~kind(X))))&
(![X]:(old(X)=>(~happy(X)|brave(X))))&
(![X]:(happy(X)=>(brave(X)<~>~kind(X))))&
(![X]:((generous(X)|kind(X))=>(calm(X)&tall(X))))&
(![X]:(calm(X)<=>(patient(X)&tall(X))))&
(![X]:((~creative(X)|~patient(X))=>kind(X)))&
(![X]:((quiet(X)|~creative(X))=>(rich(X)|~strong(X))))&
((strong(susan)|generous(susan)))&
(?[X]:((patient(X)|~funny(X))))&
(?[X]:((creative(X)&~strong(X))))&
((rich(mary)|curious(mary)))&
((humble(john)<~>tall(john)))&
(?[X]:((~old(X)&~strong(X))))&
(?[X]:(~kind(X)))&
((~generous(fred)<~>~wise(fred))) | ~happy(lucy) | [] | null | 0 |
If susan is both not tall and not humble then someone is brave or kind.
If mary is strong or calm then lucy is either calm or not kind and vice versa.
If mary is brave or not curious then someone is both not old and not generous and vice versa.
Everyone who is both patient and curious is either old or not old and vice versa.
Everyone who is both not old and not kind is not funny or not creative and vice versa.
Everyone who is not humble or wise is both tall and not kind and vice versa.
Everyone who is either not happy or not tall is curious.
Everyone who is both not generous and generous is both strong and not tall and vice versa.
Everyone who is either patient or not happy is either happy or not funny.
If someone is either kind or generous then someone is both funny and not quiet and vice versa.
If susan is either creative or not brave then susan is either generous or not kind.
If lucy is kind then paul is funny and vice versa.
If someone is both rich and kind then someone is quiet and vice versa.
Everyone who is both kind and tall is patient.
Everyone who is both not old and not calm is tall.
If someone is not kind then someone is not funny or generous and vice versa.
Someone is either not old or not kind.
Lucy is either curious or happy.
Lucy is either creative or not generous.
Paul is either not kind or quiet.
Someone is both not old and quiet.
Someone is not old.
Someone is either old or wise. | Mary is not funny. | neutral | (((~tall(susan)&~humble(susan)))=>(?[X]:((brave(X)|kind(X)))))&
(((strong(mary)|calm(mary)))<=>((calm(lucy)<~>~kind(lucy))))&
(((brave(mary)|~curious(mary)))<=>(?[X]:((~old(X)&~generous(X)))))&
(![X]:((patient(X)&curious(X))<=>(old(X)<~>~old(X))))&
(![X]:((~old(X)&~kind(X))<=>(~funny(X)|~creative(X))))&
(![X]:((~humble(X)|wise(X))<=>(tall(X)&~kind(X))))&
(![X]:((~happy(X)<~>~tall(X))=>curious(X)))&
(![X]:((~generous(X)&generous(X))<=>(strong(X)&~tall(X))))&
(![X]:((patient(X)<~>~happy(X))=>(happy(X)<~>~funny(X))))&
((?[X]:((kind(X)<~>generous(X))))<=>(?[X]:((funny(X)&~quiet(X)))))&
(((creative(susan)<~>~brave(susan)))=>((generous(susan)<~>~kind(susan))))&
((kind(lucy))<=>(funny(paul)))&
((?[X]:((rich(X)&kind(X))))<=>(?[X]:(quiet(X))))&
(![X]:((kind(X)&tall(X))=>patient(X)))&
(![X]:((~old(X)&~calm(X))=>tall(X)))&
((?[X]:(~kind(X)))<=>(?[X]:((~funny(X)|generous(X)))))&
(?[X]:((~old(X)<~>~kind(X))))&
((curious(lucy)<~>happy(lucy)))&
((creative(lucy)<~>~generous(lucy)))&
((~kind(paul)<~>quiet(paul)))&
(?[X]:((~old(X)&quiet(X))))&
(?[X]:(~old(X)))&
(?[X]:((old(X)<~>wise(X)))) | ~funny(mary) | [] | null | 0 |
Everyone who is not humble or not curious is patient or not kind and vice versa.
Everyone who is not happy or generous is not patient and vice versa.
Everyone who is strong or not happy is not creative.
If someone is old or kind then someone is either humble or curious.
If lucy is both not wise and creative then mary is not funny and vice versa.
Everyone who is patient or not kind is either not creative or tall and vice versa.
If fred is not rich or not quiet then susan is either not funny or rich and vice versa.
If susan is both tall and generous then paul is patient.
If fred is creative or not funny then someone is humble.
Everyone who is happy or humble is either calm or kind.
Everyone who is not kind is not tall and vice versa.
Everyone who is not humble is either quiet or not funny and vice versa.
Everyone who is wise or not strong is patient or not wise and vice versa.
If john is old or tall then someone is either rich or kind and vice versa.
Everyone who is either not rich or old is either not creative or not wise.
If someone is patient or not kind then lucy is not patient and vice versa.
Paul is either old or quiet.
Susan is not brave or not kind.
Susan is old or not patient.
Mary is patient.
Lucy is either not funny or not humble.
Someone is both not curious and patient.
Alice is both wise and not humble.
John is creative or kind. | Fred is strong. | neutral | (![X]:((~humble(X)|~curious(X))<=>(patient(X)|~kind(X))))&
(![X]:((~happy(X)|generous(X))<=>~patient(X)))&
(![X]:((strong(X)|~happy(X))=>~creative(X)))&
((?[X]:((old(X)|kind(X))))=>(?[X]:((humble(X)<~>curious(X)))))&
(((~wise(lucy)&creative(lucy)))<=>(~funny(mary)))&
(![X]:((patient(X)|~kind(X))<=>(~creative(X)<~>tall(X))))&
(((~rich(fred)|~quiet(fred)))<=>((~funny(susan)<~>rich(susan))))&
(((tall(susan)&generous(susan)))=>(patient(paul)))&
(((creative(fred)|~funny(fred)))=>(?[X]:(humble(X))))&
(![X]:((happy(X)|humble(X))=>(calm(X)<~>kind(X))))&
(![X]:(~kind(X)<=>~tall(X)))&
(![X]:(~humble(X)<=>(quiet(X)<~>~funny(X))))&
(![X]:((wise(X)|~strong(X))<=>(patient(X)|~wise(X))))&
(((old(john)|tall(john)))<=>(?[X]:((rich(X)<~>kind(X)))))&
(![X]:((~rich(X)<~>old(X))=>(~creative(X)<~>~wise(X))))&
((?[X]:((patient(X)|~kind(X))))<=>(~patient(lucy)))&
((old(paul)<~>quiet(paul)))&
((~brave(susan)|~kind(susan)))&
((old(susan)|~patient(susan)))&
(patient(mary))&
((~funny(lucy)<~>~humble(lucy)))&
(?[X]:((~curious(X)&patient(X))))&
((wise(alice)&~humble(alice)))&
((creative(john)|kind(john))) | strong(fred) | [] | null | 0 |
Everyone who is generous is either not tall or patient. Everyone who is not quiet is wise. If mary is funny then paul is rich or not creative and vice versa. If someone is funny or not old then susan is not wise or not generous. If fred is not brave then someone is both not rich and rich. Everyone who is both not strong and not old is either rich or wise. Everyone who is not rich or quiet is either old or not calm. If fred is funny then susan is both generous and happy and vice versa. Everyone who is not strong or not old is either not happy or curious and vice versa. If john is either wise or happy then paul is either calm or not patient and vice versa. Everyone who is not wise or old is not old and vice versa. Everyone who is either strong or calm is not quiet. If someone is quiet or not strong then someone is either creative or not funny. If someone is either not wise or not brave then someone is either wise or not generous. If alice is quiet or patient then mary is strong or quiet and vice versa. Lucy is either not curious or not kind. Someone is both creative and not calm. Alice is strong or not wise. Paul is either rich or not creative. Someone is not generous. | Paul is curious. | neutral | (![X]:(generous(X)=>(~tall(X)<~>patient(X))))&
(![X]:(~quiet(X)=>wise(X)))&
((funny(mary))<=>((rich(paul)|~creative(paul))))&
((?[X]:((funny(X)|~old(X))))=>((~wise(susan)|~generous(susan))))&
((~brave(fred))=>(?[X]:((~rich(X)&rich(X)))))&
(![X]:((~strong(X)&~old(X))=>(rich(X)<~>wise(X))))&
(![X]:((~rich(X)|quiet(X))=>(old(X)<~>~calm(X))))&
((funny(fred))<=>((generous(susan)&happy(susan))))&
(![X]:((~strong(X)|~old(X))<=>(~happy(X)<~>curious(X))))&
(((wise(john)<~>happy(john)))<=>((calm(paul)<~>~patient(paul))))&
(![X]:((~wise(X)|old(X))<=>~old(X)))&
(![X]:((strong(X)<~>calm(X))=>~quiet(X)))&
((?[X]:((quiet(X)|~strong(X))))=>(?[X]:((creative(X)<~>~funny(X)))))&
((?[X]:((~wise(X)<~>~brave(X))))=>(?[X]:((wise(X)<~>~generous(X)))))&
(((quiet(alice)|patient(alice)))<=>((strong(mary)|quiet(mary))))&
((~curious(lucy)<~>~kind(lucy)))&
(?[X]:((creative(X)&~calm(X))))&
((strong(alice)|~wise(alice)))&
((rich(paul)<~>~creative(paul)))&
(?[X]:(~generous(X))) | curious(paul) | [] | null | 0 |
Everyone who is humble or not old is both wise and generous. Everyone who is both not quiet and not happy is kind or wise and vice versa. Everyone who is creative or not curious is not curious or not kind and vice versa. If alice is either happy or generous then alice is not happy or not wise. Everyone who is not creative or not patient is not quiet. If someone is not curious or not quiet then susan is rich and vice versa. Everyone who is both not humble and creative is either rich or old and vice versa. If someone is not brave or not creative then alice is either patient or funny and vice versa. Everyone who is generous is either kind or not funny and vice versa. Everyone who is generous is calm and vice versa. Everyone who is either tall or not tall is both curious and creative and vice versa. Everyone who is calm or not funny is not funny or not generous. If someone is either curious or not happy then fred is either not funny or brave and vice versa. Everyone who is both not rich and generous is both not quiet and not old. If someone is not brave then lucy is both curious and not old. Everyone who is not kind or creative is not tall or calm and vice versa. Lucy is both tall and not funny. Someone is strong. Susan is not quiet. Someone is not happy. Someone is not wise or not curious. Someone is not tall. Someone is both not old and rich. Someone is both patient and not tall. | Alice is not strong. | neutral | (![X]:((humble(X)|~old(X))=>(wise(X)&generous(X))))&
(![X]:((~quiet(X)&~happy(X))<=>(kind(X)|wise(X))))&
(![X]:((creative(X)|~curious(X))<=>(~curious(X)|~kind(X))))&
(((happy(alice)<~>generous(alice)))=>((~happy(alice)|~wise(alice))))&
(![X]:((~creative(X)|~patient(X))=>~quiet(X)))&
((?[X]:((~curious(X)|~quiet(X))))<=>(rich(susan)))&
(![X]:((~humble(X)&creative(X))<=>(rich(X)<~>old(X))))&
((?[X]:((~brave(X)|~creative(X))))<=>((patient(alice)<~>funny(alice))))&
(![X]:(generous(X)<=>(kind(X)<~>~funny(X))))&
(![X]:(generous(X)<=>calm(X)))&
(![X]:((tall(X)<~>~tall(X))<=>(curious(X)&creative(X))))&
(![X]:((calm(X)|~funny(X))=>(~funny(X)|~generous(X))))&
((?[X]:((curious(X)<~>~happy(X))))<=>((~funny(fred)<~>brave(fred))))&
(![X]:((~rich(X)&generous(X))=>(~quiet(X)&~old(X))))&
((?[X]:(~brave(X)))=>((curious(lucy)&~old(lucy))))&
(![X]:((~kind(X)|creative(X))<=>(~tall(X)|calm(X))))&
((tall(lucy)&~funny(lucy)))&
(?[X]:(strong(X)))&
(~quiet(susan))&
(?[X]:(~happy(X)))&
(?[X]:((~wise(X)|~curious(X))))&
(?[X]:(~tall(X)))&
(?[X]:((~old(X)&rich(X))))&
(?[X]:((patient(X)&~tall(X)))) | ~strong(alice) | [] | null | 0 |
Everyone who is wise is generous.
Everyone who is humble is either wise or rich.
Everyone who is both creative and not generous is wise and vice versa.
Everyone who is either not patient or not curious is both not humble and funny and vice versa.
Everyone who is not happy or humble is both strong and not rich and vice versa.
Everyone who is wise or not creative is either humble or brave.
If mary is not humble or quiet then susan is strong and vice versa.
Everyone who is both not brave and humble is not happy and vice versa.
Everyone who is not generous or funny is both not old and not curious.
If someone is not brave then john is not brave and vice versa.
Everyone who is humble is not rich.
Everyone who is both not patient and not old is either not quiet or not curious and vice versa.
Everyone who is both patient and calm is kind or not quiet.
If someone is both not generous and not old then mary is brave.
If fred is either strong or patient then mary is quiet and vice versa.
Someone is either not funny or brave.
Someone is either not patient or not strong.
Someone is not creative.
Someone is not generous.
Someone is either not creative or tall.
Someone is both funny and not old.
Someone is either wise or calm.
Someone is not funny. | Susan is humble. | contradiction | (![X]:(wise(X)=>generous(X)))&
(![X]:(humble(X)=>(wise(X)<~>rich(X))))&
(![X]:((creative(X)&~generous(X))<=>wise(X)))&
(![X]:((~patient(X)<~>~curious(X))<=>(~humble(X)&funny(X))))&
(![X]:((~happy(X)|humble(X))<=>(strong(X)&~rich(X))))&
(![X]:((wise(X)|~creative(X))=>(humble(X)<~>brave(X))))&
(((~humble(mary)|quiet(mary)))<=>(strong(susan)))&
(![X]:((~brave(X)&humble(X))<=>~happy(X)))&
(![X]:((~generous(X)|funny(X))=>(~old(X)&~curious(X))))&
((?[X]:(~brave(X)))<=>(~brave(john)))&
(![X]:(humble(X)=>~rich(X)))&
(![X]:((~patient(X)&~old(X))<=>(~quiet(X)<~>~curious(X))))&
(![X]:((patient(X)&calm(X))=>(kind(X)|~quiet(X))))&
((?[X]:((~generous(X)&~old(X))))=>(brave(mary)))&
(((strong(fred)<~>patient(fred)))<=>(quiet(mary)))&
(?[X]:((~funny(X)<~>brave(X))))&
(?[X]:((~patient(X)<~>~strong(X))))&
(?[X]:(~creative(X)))&
(?[X]:(~generous(X)))&
(?[X]:((~creative(X)<~>tall(X))))&
(?[X]:((funny(X)&~old(X))))&
(?[X]:((wise(X)<~>calm(X))))&
(?[X]:(~funny(X))) | humble(susan) | [
"p0",
"p1",
"p2",
"p4",
"hypothesis"
] | % SZS status Unsatisfiable for 4116821110227591302754845
% SZS output start Proof for 4116821110227591302754845
1. ! [X0] : (wise(X0) => generous(X0)) [input p0]
2. ! [X0] : (humble(X0) => (wise(X0) <~> rich(X0))) [input p1]
3. ! [X0] : ((~generous(X0) & creative(X0)) <=> wise(X0)) [input p2]
5. ! [X0] : ((humble(X0) | ~happy(X0)) <=> (~rich(X0) & strong(X0))) [input p4]
24. humble(susan) [input hypothesis]
26. ! [X0] : (generous(X0) | ~wise(X0)) [ennf transformation 1]
27. ! [X0] : ((wise(X0) <~> rich(X0)) | ~humble(X0)) [ennf transformation 2]
32. ! [X0] : (((~rich(X0) | ~wise(X0)) & (rich(X0) | wise(X0))) | ~humble(X0)) [nnf transformation 27]
33. ! [X0] : (((~generous(X0) & creative(X0)) | ~wise(X0)) & (wise(X0) | (generous(X0) | ~creative(X0)))) [nnf transformation 3]
34. ! [X0] : (((~generous(X0) & creative(X0)) | ~wise(X0)) & (wise(X0) | generous(X0) | ~creative(X0))) [flattening 33]
37. ! [X0] : (((humble(X0) | ~happy(X0)) | (rich(X0) | ~strong(X0))) & ((~rich(X0) & strong(X0)) | (~humble(X0) & happy(X0)))) [nnf transformation 5]
38. ! [X0] : ((humble(X0) | ~happy(X0) | rich(X0) | ~strong(X0)) & ((~rich(X0) & strong(X0)) | (~humble(X0) & happy(X0)))) [flattening 37]
71. ~wise(X0) | generous(X0) [cnf transformation 26]
72. ~humble(X0) | wise(X0) | rich(X0) [cnf transformation 32]
76. ~generous(X0) | ~wise(X0) [cnf transformation 34]
86. ~rich(X0) | ~humble(X0) [cnf transformation 38]
129. humble(susan) [cnf transformation 24]
130. ~wise(X0) [subsumption resolution 76,71]
224. wise(susan) | rich(susan) [resolution 72,129]
225. rich(susan) [subsumption resolution 224,130]
226. ~humble(susan) [resolution 225,86]
228. $false [subsumption resolution 226,129]
% SZS output end Proof for 4116821110227591302754845
% ------------------------------
% Version: Vampire 4.8 (commit 8d999c135 on 2023-07-12 16:43:10 +0000)
% Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% Termination reason: Refutation
% Memory used [KB]: 5117
% Time elapsed: 0.027 s
% ------------------------------
% ------------------------------
| 0 |
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